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estimators</title> <meta name="description" content="Search results for: robust estimators"> <meta name="keywords" content="robust estimators"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="robust estimators"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1550</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: robust estimators</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1550</span> Alternative Robust Estimators for the Shape Parameters of the Burr XII Distribution</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fatma%20Zehra%20Do%C4%9Fru">Fatma Zehra Doğru</a>, <a href="https://publications.waset.org/abstracts/search?q=Olcay%20Arslan"> Olcay Arslan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we propose alternative robust estimators for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=burr%20xii%20distribution" title="burr xii distribution">burr xii distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20estimator" title=" robust estimator"> robust estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=m-estimator" title=" m-estimator"> m-estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=least%20squares" title=" least squares"> least squares</a> </p> <a href="https://publications.waset.org/abstracts/30038/alternative-robust-estimators-for-the-shape-parameters-of-the-burr-xii-distribution" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30038.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">428</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1549</span> Introduction of Robust Multivariate Process Capability Indices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Behrooz%20Khalilloo">Behrooz Khalilloo</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamid%20Shahriari"> Hamid Shahriari</a>, <a href="https://publications.waset.org/abstracts/search?q=Emad%20Roghanian"> Emad Roghanian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Process capability indices (PCIs) are important concepts of statistical quality control and measure the capability of processes and how much processes are meeting certain specifications. An important issue in statistical quality control is parameter estimation. Under the assumption of multivariate normality, the distribution parameters, mean vector and variance-covariance matrix must be estimated, when they are unknown. Classic estimation methods like method of moment estimation (MME) or maximum likelihood estimation (MLE) makes good estimation of the population parameters when data are not contaminated. But when outliers exist in the data, MME and MLE make weak estimators of the population parameters. So we need some estimators which have good estimation in the presence of outliers. In this work robust M-estimators for estimating these parameters are used and based on robust parameter estimators, robust process capability indices are introduced. The performances of these robust estimators in the presence of outliers and their effects on process capability indices are evaluated by real and simulated multivariate data. The results indicate that the proposed robust capability indices perform much better than the existing process capability indices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multivariate%20process%20capability%20indices" title="multivariate process capability indices">multivariate process capability indices</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20M-estimator" title=" robust M-estimator"> robust M-estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=outlier" title=" outlier"> outlier</a>, <a href="https://publications.waset.org/abstracts/search?q=multivariate%20quality%20control" title=" multivariate quality control"> multivariate quality control</a>, <a href="https://publications.waset.org/abstracts/search?q=statistical%20quality%20control" title=" statistical quality control"> statistical quality control</a> </p> <a href="https://publications.waset.org/abstracts/81586/introduction-of-robust-multivariate-process-capability-indices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81586.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">283</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1548</span> Comparing Xbar Charts: Conventional versus Reweighted Robust Estimation Methods for Univariate Data Sets</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ece%20Cigdem%20Mutlu">Ece Cigdem Mutlu</a>, <a href="https://publications.waset.org/abstracts/search?q=Burak%20Alakent"> Burak Alakent</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Maintaining the quality of manufactured products at a desired level depends on the stability of process dispersion and location parameters and detection of perturbations in these parameters as promptly as possible. Shewhart control chart is the most widely used technique in statistical process monitoring to monitor the quality of products and control process mean and variability. In the application of Xbar control charts, sample standard deviation and sample mean are known to be the most efficient conventional estimators in determining process dispersion and location parameters, respectively, based on the assumption of independent and normally distributed datasets. On the other hand, there is no guarantee that the real-world data would be normally distributed. In the cases of estimated process parameters from Phase I data clouded with outliers, efficiency of traditional estimators is significantly reduced, and performance of Xbar charts are undesirably low, e.g. occasional outliers in the rational subgroups in Phase I data set may considerably affect the sample mean and standard deviation, resulting a serious delay in detection of inferior products in Phase II. For more efficient application of control charts, it is required to use robust estimators against contaminations, which may exist in Phase I. In the current study, we present a simple approach to construct robust Xbar control charts using average distance to the median, Qn-estimator of scale, M-estimator of scale with logistic psi-function in the estimation of process dispersion parameter, and Harrell-Davis qth quantile estimator, Hodge-Lehmann estimator and M-estimator of location with Huber psi-function and logistic psi-function in the estimation of process location parameter. Phase I efficiency of proposed estimators and Phase II performance of Xbar charts constructed from these estimators are compared with the conventional mean and standard deviation statistics both under normality and against diffuse-localized and symmetric-asymmetric contaminations using 50,000 Monte Carlo simulations on MATLAB. Consequently, it is found that robust estimators yield parameter estimates with higher efficiency against all types of contaminations, and Xbar charts constructed using robust estimators have higher power in detecting disturbances, compared to conventional methods. Additionally, utilizing individuals charts to screen outlier subgroups and employing different combination of dispersion and location estimators on subgroups and individual observations are found to improve the performance of Xbar charts. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=average%20run%20length" title="average run length">average run length</a>, <a href="https://publications.waset.org/abstracts/search?q=M-estimators" title=" M-estimators"> M-estimators</a>, <a href="https://publications.waset.org/abstracts/search?q=quality%20control" title=" quality control"> quality control</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20estimators" title=" robust estimators"> robust estimators</a> </p> <a href="https://publications.waset.org/abstracts/79020/comparing-xbar-charts-conventional-versus-reweighted-robust-estimation-methods-for-univariate-data-sets" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79020.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">190</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1547</span> Some Generalized Multivariate Estimators for Population Mean under Multi Phase Stratified Systematic Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muqaddas%20Javed">Muqaddas Javed</a>, <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Hanif"> Muhammad Hanif</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The generalized multivariate ratio and regression type estimators for population mean are suggested under multi-phase stratified systematic sampling (MPSSS) using multi auxiliary information. Estimators are developed under the two different situations of availability of auxiliary information. The expressions of bias and mean square error (MSE) are developed. Special cases of suggested estimators are also discussed and simulation study is conducted to observe the performance of estimators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20estimators" title="generalized estimators">generalized estimators</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-phase%20sampling" title=" multi-phase sampling"> multi-phase sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=stratified%20random%20sampling" title=" stratified random sampling"> stratified random sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=systematic%20sampling" title=" systematic sampling"> systematic sampling</a> </p> <a href="https://publications.waset.org/abstracts/27296/some-generalized-multivariate-estimators-for-population-mean-under-multi-phase-stratified-systematic-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27296.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">729</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1546</span> Robust Shrinkage Principal Component Parameter Estimator for Combating Multicollinearity and Outliers’ Problems in a Poisson Regression Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arum%20Kingsley%20Chinedu">Arum Kingsley Chinedu</a>, <a href="https://publications.waset.org/abstracts/search?q=Ugwuowo%20Fidelis%20Ifeanyi"> Ugwuowo Fidelis Ifeanyi</a>, <a href="https://publications.waset.org/abstracts/search?q=Oranye%20Henrietta%20Ebele"> Oranye Henrietta Ebele</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Poisson regression model (PRM) is a nonlinear model that belongs to the exponential family of distribution. PRM is suitable for studying count variables using appropriate covariates and sometimes experiences the problem of multicollinearity in the explanatory variables and outliers on the response variable. This study aims to address the problem of multicollinearity and outliers jointly in a Poisson regression model. We developed an estimator called the robust modified jackknife PCKL parameter estimator by combining the principal component estimator, modified jackknife KL and transformed M-estimator estimator to address both problems in a PRM. The superiority conditions for this estimator were established, and the properties of the estimator were also derived. The estimator inherits the characteristics of the combined estimators, thereby making it efficient in addressing both problems. And will also be of immediate interest to the research community and advance this study in terms of novelty compared to other studies undertaken in this area. The performance of the estimator (robust modified jackknife PCKL) with other existing estimators was compared using mean squared error (MSE) as a performance evaluation criterion through a Monte Carlo simulation study and the use of real-life data. The results of the analytical study show that the estimator outperformed other existing estimators compared with by having the smallest MSE across all sample sizes, different levels of correlation, percentages of outliers and different numbers of explanatory variables. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=jackknife%20modified%20KL" title="jackknife modified KL">jackknife modified KL</a>, <a href="https://publications.waset.org/abstracts/search?q=outliers" title=" outliers"> outliers</a>, <a href="https://publications.waset.org/abstracts/search?q=multicollinearity" title=" multicollinearity"> multicollinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=principal%20component" title=" principal component"> principal component</a>, <a href="https://publications.waset.org/abstracts/search?q=transformed%20M-estimator." title=" transformed M-estimator."> transformed M-estimator.</a> </p> <a href="https://publications.waset.org/abstracts/183536/robust-shrinkage-principal-component-parameter-estimator-for-combating-multicollinearity-and-outliers-problems-in-a-poisson-regression-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/183536.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">66</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1545</span> A Generalized Family of Estimators for Estimation of Unknown Population Variance in Simple Random Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saba%20Riaz">Saba Riaz</a>, <a href="https://publications.waset.org/abstracts/search?q=Syed%20A.%20Hussain"> Syed A. Hussain</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=study%20variable" title="study variable">study variable</a>, <a href="https://publications.waset.org/abstracts/search?q=auxiliary%20variable" title=" auxiliary variable"> auxiliary variable</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20population%20variance" title=" finite population variance"> finite population variance</a>, <a href="https://publications.waset.org/abstracts/search?q=bias" title=" bias"> bias</a>, <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20variance" title=" asymptotic variance"> asymptotic variance</a>, <a href="https://publications.waset.org/abstracts/search?q=percent%20relative%20efficiency" title=" percent relative efficiency"> percent relative efficiency</a> </p> <a href="https://publications.waset.org/abstracts/87115/a-generalized-family-of-estimators-for-estimation-of-unknown-population-variance-in-simple-random-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/87115.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">225</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1544</span> Model Averaging in a Multiplicative Heteroscedastic Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alan%20Wan">Alan Wan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In recent years, the body of literature on frequentist model averaging in statistics has grown significantly. Most of this work focuses on models with different mean structures but leaves out the variance consideration. In this paper, we consider a regression model with multiplicative heteroscedasticity and develop a model averaging method that combines maximum likelihood estimators of unknown parameters in both the mean and variance functions of the model. Our weight choice criterion is based on a minimisation of a plug-in estimator of the model average estimator's squared prediction risk. We prove that the new estimator possesses an asymptotic optimality property. Our investigation of finite-sample performance by simulations demonstrates that the new estimator frequently exhibits very favourable properties compared to some existing heteroscedasticity-robust model average estimators. The model averaging method hedges against the selection of very bad models and serves as a remedy to variance function misspecification, which often discourages practitioners from modeling heteroscedasticity altogether. The proposed model average estimator is applied to the analysis of two real data sets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=heteroscedasticity-robust" title="heteroscedasticity-robust">heteroscedasticity-robust</a>, <a href="https://publications.waset.org/abstracts/search?q=model%20averaging" title=" model averaging"> model averaging</a>, <a href="https://publications.waset.org/abstracts/search?q=multiplicative%20heteroscedasticity" title=" multiplicative heteroscedasticity"> multiplicative heteroscedasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=plug-in" title=" plug-in"> plug-in</a>, <a href="https://publications.waset.org/abstracts/search?q=squared%20prediction%20risk" title=" squared prediction risk"> squared prediction risk</a> </p> <a href="https://publications.waset.org/abstracts/68733/model-averaging-in-a-multiplicative-heteroscedastic-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/68733.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">385</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1543</span> Point Estimation for the Type II Generalized Logistic Distribution Based on Progressively Censored Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rana%20Rimawi">Rana Rimawi</a>, <a href="https://publications.waset.org/abstracts/search?q=Ayman%20Baklizi"> Ayman Baklizi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=point%20estimation" title="point estimation">point estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=type%20II%20generalized%20logistic%20distribution" title=" type II generalized logistic distribution"> type II generalized logistic distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=progressive%20censoring" title=" progressive censoring"> progressive censoring</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood%20estimation" title=" maximum likelihood estimation"> maximum likelihood estimation</a> </p> <a href="https://publications.waset.org/abstracts/142979/point-estimation-for-the-type-ii-generalized-logistic-distribution-based-on-progressively-censored-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142979.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">198</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1542</span> Comparative Study of Estimators of Population Means in Two Phase Sampling in the Presence of Non-Response</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Syed%20Ali%20Taqi">Syed Ali Taqi</a>, <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Ismail"> Muhammad Ismail</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A comparative study of estimators of population means in two phase sampling in the presence of non-response when Unknown population means of the auxiliary variable(s) and incomplete information of study variable y as well as of auxiliary variable(s) is made. Three real data sets of University students, hospital and unemployment are used for comparison of all the available techniques in two phase sampling in the presence of non-response with the newly generalized ratio estimators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=two-phase%20sampling" title="two-phase sampling">two-phase sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=ratio%20estimator" title=" ratio estimator"> ratio estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20estimator" title=" product estimator"> product estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20estimators" title=" generalized estimators"> generalized estimators</a> </p> <a href="https://publications.waset.org/abstracts/79636/comparative-study-of-estimators-of-population-means-in-two-phase-sampling-in-the-presence-of-non-response" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79636.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">233</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1541</span> Estimation of Population Mean under Random Non-Response in Two-Phase Successive Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Khalid">M. Khalid</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20N.%20Singh"> G. N. Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have considered the problem of estimation for population mean, on current (second) occasion in the presence of random non response in two-occasion successive sampling under two phase set-up. Modified exponential type estimators have been proposed, and their properties are studied under the assumptions that numbers of sampling units follow a distribution due to random non response situations. The performances of the proposed estimators are compared with linear combinations of two estimators, (a) sample mean estimator for fresh sample and (b) ratio estimator for matched sample under the complete response situations. Results are demonstrated through empirical studies which present the effectiveness of the proposed estimators. Suitable recommendations have been made to the survey practitioners. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=successive%20sampling" title="successive sampling">successive sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20non-response" title=" random non-response"> random non-response</a>, <a href="https://publications.waset.org/abstracts/search?q=auxiliary%20variable" title=" auxiliary variable"> auxiliary variable</a>, <a href="https://publications.waset.org/abstracts/search?q=bias" title=" bias"> bias</a>, <a href="https://publications.waset.org/abstracts/search?q=mean%20square%20error" title=" mean square error"> mean square error</a> </p> <a href="https://publications.waset.org/abstracts/78773/estimation-of-population-mean-under-random-non-response-in-two-phase-successive-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78773.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">521</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1540</span> Estimation of Population Mean Using Characteristics of Poisson Distribution: An Application to Earthquake Data</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prayas%20Sharma">Prayas Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposed a generalized class of estimators, an exponential class of estimators based on the adaption of Sharma and Singh (2015) and Solanki and Singh (2013), and a simple difference estimator for estimating unknown population mean in the case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived from the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), the exponential class of estimator, is always more efficient than the usual estimator, ratio, product, exponential ratio, and exponential product type estimators and equally efficient to simple difference estimator. Moreover, the adapted version of Sharma and Singh's (2015) estimator is always more efficient than all the estimators available in the literature. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with an application to earthquake data of Turkey. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=auxiliary%20attribute" title="auxiliary attribute">auxiliary attribute</a>, <a href="https://publications.waset.org/abstracts/search?q=point%20bi-serial" title=" point bi-serial"> point bi-serial</a>, <a href="https://publications.waset.org/abstracts/search?q=mean%20square%20error" title=" mean square error"> mean square error</a>, <a href="https://publications.waset.org/abstracts/search?q=simple%20random%20sampling" title=" simple random sampling"> simple random sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=Poisson%20distribution" title=" Poisson distribution"> Poisson distribution</a> </p> <a href="https://publications.waset.org/abstracts/171049/estimation-of-population-mean-using-characteristics-of-poisson-distribution-an-application-to-earthquake-data" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171049.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">156</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1539</span> Estimation of Population Mean under Random Non-Response in Two-Occasion Successive Sampling </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Khalid">M. Khalid</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20N.%20Singh"> G. N. Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we have considered the problems of estimation for the population mean on current (second) occasion in two-occasion successive sampling under random non-response situations. Some modified exponential type estimators have been proposed and their properties are studied under the assumptions that the number of sampling unit follows a discrete distribution due to random non-response situations. The performances of the proposed estimators are compared with linear combinations of two estimators, (a) sample mean estimator for fresh sample and (b) ratio estimator for matched sample under the complete response situations. Results are demonstrated through empirical studies which present the effectiveness of the proposed estimators. Suitable recommendations have been made to the survey practitioners. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modified%20exponential%20estimator" title="modified exponential estimator">modified exponential estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=successive%20sampling" title=" successive sampling"> successive sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20non-response" title=" random non-response"> random non-response</a>, <a href="https://publications.waset.org/abstracts/search?q=auxiliary%20variable" title=" auxiliary variable"> auxiliary variable</a>, <a href="https://publications.waset.org/abstracts/search?q=bias" title=" bias"> bias</a>, <a href="https://publications.waset.org/abstracts/search?q=mean%20square%20error" title=" mean square error"> mean square error</a> </p> <a href="https://publications.waset.org/abstracts/85408/estimation-of-population-mean-under-random-non-response-in-two-occasion-successive-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85408.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">349</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1538</span> Finite Sample Inferences for Weak Instrument Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gubhinder%20Kundhi">Gubhinder Kundhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20Rilstone"> Paul Rilstone</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. Finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bootstrap" title="bootstrap">bootstrap</a>, <a href="https://publications.waset.org/abstracts/search?q=Instrumental%20Variable" title=" Instrumental Variable"> Instrumental Variable</a>, <a href="https://publications.waset.org/abstracts/search?q=Edgeworth%20expansions" title=" Edgeworth expansions"> Edgeworth expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=Saddlepoint%20expansions" title=" Saddlepoint expansions"> Saddlepoint expansions</a> </p> <a href="https://publications.waset.org/abstracts/46824/finite-sample-inferences-for-weak-instrument-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46824.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">310</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1537</span> Ratio Type Estimators for the Estimation of Population Coefficient of Variation under Two-Stage Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Jabbar">Muhammad Jabbar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we propose two ratio and ratio type exponential estimator for the estimation of population coefficient of variation using the auxiliary information under two-stage sampling. The properties of these estimators are derived up to first order of approximation. The efficiency conditions under which suggested estimator are more efficient, are obtained. Numerical and simulated studies are conducted to support the superiority of the estimators. Theoretically and numerically, we have found that our proposed estimator is always more efficient as compared to its competitor estimator. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=two-stage%20sampling" title="two-stage sampling">two-stage sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=coefficient%20of%20variation" title=" coefficient of variation"> coefficient of variation</a>, <a href="https://publications.waset.org/abstracts/search?q=ratio%20type%20exponential%20estimator" title=" ratio type exponential estimator"> ratio type exponential estimator</a> </p> <a href="https://publications.waset.org/abstracts/21936/ratio-type-estimators-for-the-estimation-of-population-coefficient-of-variation-under-two-stage-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21936.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">529</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1536</span> Robust Variogram Fitting Using Non-Linear Rank-Based Estimators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hazem%20M.%20Al-Mofleh">Hazem M. Al-Mofleh</a>, <a href="https://publications.waset.org/abstracts/search?q=John%20E.%20Daniels"> John E. Daniels</a>, <a href="https://publications.waset.org/abstracts/search?q=Joseph%20W.%20McKean"> Joseph W. McKean</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper numerous robust fitting procedures are considered in estimating spatial variograms. In spatial statistics, the conventional variogram fitting procedure (non-linear weighted least squares) suffers from the same outlier problem that has plagued this method from its inception. Even a 3-parameter model, like the variogram, can be adversely affected by a single outlier. This paper uses the Hogg-Type adaptive procedures to select an optimal score function for a rank-based estimator for these non-linear models. Numeric examples and simulation studies will demonstrate the robustness, utility, efficiency, and validity of these estimates. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20relative%20efficiency" title="asymptotic relative efficiency">asymptotic relative efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20rank-based" title=" non-linear rank-based"> non-linear rank-based</a>, <a href="https://publications.waset.org/abstracts/search?q=rank%20estimates" title=" rank estimates"> rank estimates</a>, <a href="https://publications.waset.org/abstracts/search?q=variogram" title=" variogram"> variogram</a> </p> <a href="https://publications.waset.org/abstracts/43980/robust-variogram-fitting-using-non-linear-rank-based-estimators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43980.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">431</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1535</span> Estimation of the Mean of the Selected Population</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kalu%20Ram%20Meena">Kalu Ram Meena</a>, <a href="https://publications.waset.org/abstracts/search?q=Aditi%20Kar%20Gangopadhyay"> Aditi Kar Gangopadhyay</a>, <a href="https://publications.waset.org/abstracts/search?q=Satrajit%20Mandal"> Satrajit Mandal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two normal populations with different means and same variance are considered, where the variances are known. The population with the smaller sample mean is selected. Various estimators are constructed for the mean of the selected normal population. Finally, they are compared with respect to the bias and MSE risks by the method of Monte-Carlo simulation and their performances are analysed with the help of graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=estimation%20after%20selection" title="estimation after selection">estimation after selection</a>, <a href="https://publications.waset.org/abstracts/search?q=Brewster-Zidek%20technique" title=" Brewster-Zidek technique"> Brewster-Zidek technique</a>, <a href="https://publications.waset.org/abstracts/search?q=estimators" title=" estimators"> estimators</a>, <a href="https://publications.waset.org/abstracts/search?q=selected%20populations" title=" selected populations"> selected populations</a> </p> <a href="https://publications.waset.org/abstracts/17179/estimation-of-the-mean-of-the-selected-population" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17179.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">512</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1534</span> Parameter Estimation for the Mixture of Generalized Gamma Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wikanda%20Phaphan">Wikanda Phaphan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20gradient%20method" title="conjugate gradient method">conjugate gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=quasi-Newton%20method" title=" quasi-Newton method"> quasi-Newton method</a>, <a href="https://publications.waset.org/abstracts/search?q=EM-algorithm" title=" EM-algorithm"> EM-algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20gamma%20distribution" title=" generalized gamma distribution"> generalized gamma distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=length%20biased%20generalized%20gamma%20distribution" title=" length biased generalized gamma distribution"> length biased generalized gamma distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood%20method" title=" maximum likelihood method"> maximum likelihood method</a> </p> <a href="https://publications.waset.org/abstracts/81404/parameter-estimation-for-the-mixture-of-generalized-gamma-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/81404.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">219</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1533</span> Minimizing the Impact of Covariate Detection Limit in Logistic Regression</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shahadut%20Hossain">Shahadut Hossain</a>, <a href="https://publications.waset.org/abstracts/search?q=Jacek%20Wesolowski"> Jacek Wesolowski</a>, <a href="https://publications.waset.org/abstracts/search?q=Zahirul%20Hoque"> Zahirul Hoque</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In many epidemiological and environmental studies covariate measurements are subject to the detection limit. In most applications, covariate measurements are usually truncated from below which is known as left-truncation. Because the measuring device, which we use to measure the covariate, fails to detect values falling below the certain threshold. In regression analyses, it causes inflated bias and inaccurate mean squared error (MSE) to the estimators. This paper suggests a response-based regression calibration method to correct the deleterious impact introduced by the covariate detection limit in the estimators of the parameters of simple logistic regression model. Compared to the maximum likelihood method, the proposed method is computationally simpler, and hence easier to implement. It is robust to the violation of distributional assumption about the covariate of interest. In producing correct inference, the performance of the proposed method compared to the other competing methods has been investigated through extensive simulations. A real-life application of the method is also shown using data from a population-based case-control study of non-Hodgkin lymphoma. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=environmental%20exposure" title="environmental exposure">environmental exposure</a>, <a href="https://publications.waset.org/abstracts/search?q=detection%20limit" title=" detection limit"> detection limit</a>, <a href="https://publications.waset.org/abstracts/search?q=left%20truncation" title=" left truncation"> left truncation</a>, <a href="https://publications.waset.org/abstracts/search?q=bias" title=" bias"> bias</a>, <a href="https://publications.waset.org/abstracts/search?q=ad-hoc%20substitution" title=" ad-hoc substitution"> ad-hoc substitution</a> </p> <a href="https://publications.waset.org/abstracts/55567/minimizing-the-impact-of-covariate-detection-limit-in-logistic-regression" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55567.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">236</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1532</span> Bayes Estimation of Parameters of Binomial Type Rayleigh Class Software Reliability Growth Model using Non-informative Priors</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Singh">Rajesh Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Kailash%20Kale"> Kailash Kale </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the Binomial process type occurrence of software failures is considered and failure intensity has been characterized by one parameter Rayleigh class Software Reliability Growth Model (SRGM). The proposed SRGM is mathematical function of parameters namely; total number of failures i.e. η-0 and scale parameter i.e. η-1. It is assumed that very little or no information is available about both these parameters and then considering non-informative priors for both these parameters, the Bayes estimators for the parameters η-0 and η-1 have been obtained under square error loss function. The proposed Bayes estimators are compared with their corresponding maximum likelihood estimators on the basis of risk efficiencies obtained by Monte Carlo simulation technique. It is concluded that both the proposed Bayes estimators of total number of failures and scale parameter perform well for proper choice of execution time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=binomial%20process" title="binomial process">binomial process</a>, <a href="https://publications.waset.org/abstracts/search?q=non-informative%20prior" title=" non-informative prior"> non-informative prior</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood%20estimator%20%28MLE%29" title=" maximum likelihood estimator (MLE)"> maximum likelihood estimator (MLE)</a>, <a href="https://publications.waset.org/abstracts/search?q=rayleigh%20class" title=" rayleigh class"> rayleigh class</a>, <a href="https://publications.waset.org/abstracts/search?q=software%20reliability%20growth%20model%20%28SRGM%29" title=" software reliability growth model (SRGM)"> software reliability growth model (SRGM)</a> </p> <a href="https://publications.waset.org/abstracts/8925/bayes-estimation-of-parameters-of-binomial-type-rayleigh-class-software-reliability-growth-model-using-non-informative-priors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8925.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">389</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1531</span> Improved Estimation Strategies of Sensitive Characteristics Using Scrambled Response Techniques in Successive Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Suman">S. Suman</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20N.%20Singh"> G. N. Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research work is an effort to analyse the consequences of scrambled response technique to estimate the current population mean in two-occasion successive sampling when the characteristic of interest is sensitive in nature. The generalized estimation procedures have been proposed using sensitive auxiliary variables under additive and multiplicative scramble models. The properties of resultant estimators have been deeply examined. Simulation, as well as empirical studies, are carried out to evaluate the performances of the proposed estimators with respect to other competent estimators. The results of our studies suggest that the proposed estimation procedures are highly effective under the presence of non-response situation. The result of this study also suggests that additive scrambled response model is a better choice in the perspective of cost of the survey and privacy of the respondents. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=scrambled%20response" title="scrambled response">scrambled response</a>, <a href="https://publications.waset.org/abstracts/search?q=sensitive%20characteristic" title=" sensitive characteristic"> sensitive characteristic</a>, <a href="https://publications.waset.org/abstracts/search?q=successive%20sampling" title=" successive sampling"> successive sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=optimum%20replacement%20strategy" title=" optimum replacement strategy"> optimum replacement strategy</a> </p> <a href="https://publications.waset.org/abstracts/95355/improved-estimation-strategies-of-sensitive-characteristics-using-scrambled-response-techniques-in-successive-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/95355.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">178</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1530</span> Bayesian Approach for Moving Extremes Ranked Set Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Said%20Ali%20Al-Hadhrami">Said Ali Al-Hadhrami</a>, <a href="https://publications.waset.org/abstracts/search?q=Amer%20Ibrahim%20Al-Omari"> Amer Ibrahim Al-Omari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, Bayesian estimation for the mean of exponential distribution is considered using Moving Extremes Ranked Set Sampling (MERSS). Three priors are used; Jeffery, conjugate and constant using MERSS and Simple Random Sampling (SRS). Some properties of the proposed estimators are investigated. It is found that the suggested estimators using MERSS are more efficient than its counterparts based on SRS. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bayesian" title="Bayesian">Bayesian</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=moving%20extreme%20ranked%20set%20sampling" title=" moving extreme ranked set sampling"> moving extreme ranked set sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=ranked%20set%20sampling" title=" ranked set sampling"> ranked set sampling</a> </p> <a href="https://publications.waset.org/abstracts/30733/bayesian-approach-for-moving-extremes-ranked-set-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30733.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">514</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1529</span> A Comparative Study of Additive and Nonparametric Regression Estimators and Variable Selection Procedures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adriano%20Z.%20Zambom">Adriano Z. Zambom</a>, <a href="https://publications.waset.org/abstracts/search?q=Preethi%20Ravikumar"> Preethi Ravikumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the biggest challenges in nonparametric regression is the curse of dimensionality. Additive models are known to overcome this problem by estimating only the individual additive effects of each covariate. However, if the model is misspecified, the accuracy of the estimator compared to the fully nonparametric one is unknown. In this work the efficiency of completely nonparametric regression estimators such as the Loess is compared to the estimators that assume additivity in several situations, including additive and non-additive regression scenarios. The comparison is done by computing the oracle mean square error of the estimators with regards to the true nonparametric regression function. Then, a backward elimination selection procedure based on the Akaike Information Criteria is proposed, which is computed from either the additive or the nonparametric model. Simulations show that if the additive model is misspecified, the percentage of time it fails to select important variables can be higher than that of the fully nonparametric approach. A dimension reduction step is included when nonparametric estimator cannot be computed due to the curse of dimensionality. Finally, the Boston housing dataset is analyzed using the proposed backward elimination procedure and the selected variables are identified. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=additive%20model" title="additive model">additive model</a>, <a href="https://publications.waset.org/abstracts/search?q=nonparametric%20regression" title=" nonparametric regression"> nonparametric regression</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20selection" title=" variable selection"> variable selection</a>, <a href="https://publications.waset.org/abstracts/search?q=Akaike%20Information%20Criteria" title=" Akaike Information Criteria"> Akaike Information Criteria</a> </p> <a href="https://publications.waset.org/abstracts/56158/a-comparative-study-of-additive-and-nonparametric-regression-estimators-and-variable-selection-procedures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56158.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">265</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1528</span> Study of Cavitation Erosion of Pump-Storage Hydro Power Plant Prototype</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tine%20Cenci%C4%8D">Tine Cencič</a>, <a href="https://publications.waset.org/abstracts/search?q=Marko%20Ho%C4%8Devar"> Marko Hočevar</a>, <a href="https://publications.waset.org/abstracts/search?q=Brane%20%C5%A0irok"> Brane Širok</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An experimental investigation has been made to detect cavitation in pump–storage hydro power plant prototype suffering from cavitation in pump mode. Vibrations and acoustic emission on the housing of turbine bearing and pressure fluctuations in the draft tube were measured and the corresponding signals have been recorded and analyzed. The analysis was based on the analysis of high-frequency content of measured variables. The pump-storage hydro power plant prototype has been operated at various input loads and Thoma numbers. Several estimators of cavitation were evaluated according to coefficient of determination between Thoma number and cavitation estimators. The best results were achieved with a compound discharge coefficient cavitation estimator. Cavitation estimators were evaluated in several intervals of frequencies. Also, a prediction of cavitation erosion was made in order to choose the appropriate maintenance and repair periods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cavitation%20erosion" title="cavitation erosion">cavitation erosion</a>, <a href="https://publications.waset.org/abstracts/search?q=turbine" title=" turbine"> turbine</a>, <a href="https://publications.waset.org/abstracts/search?q=cavitation%20measurement" title=" cavitation measurement"> cavitation measurement</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid%20dynamics" title=" fluid dynamics"> fluid dynamics</a> </p> <a href="https://publications.waset.org/abstracts/8147/study-of-cavitation-erosion-of-pump-storage-hydro-power-plant-prototype" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8147.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">415</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1527</span> Synthesis of the Robust Regulators on the Basis of the Criterion of the Maximum Stability Degree</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20A.%20Gayvoronsky">S. A. Gayvoronsky</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20A.%20Ezangina"> T. A. Ezangina </a> </p> <p class="card-text"><strong>Abstract:</strong></p> The robust control system objects with interval-undermined parameters is considers in this paper. Initial information about the system is its characteristic polynomial with interval coefficients. On the basis of coefficient estimations of quality indices and criterion of the maximum stability degree, the methods of synthesis of a robust regulator parametric is developed. The example of the robust stabilization system synthesis of the rope tension is given in this article. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=interval%20polynomial" title="interval polynomial">interval polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=controller%20synthesis" title=" controller synthesis"> controller synthesis</a>, <a href="https://publications.waset.org/abstracts/search?q=analysis%20of%20quality%20factors" title=" analysis of quality factors"> analysis of quality factors</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20degree%20of%20stability" title=" maximum degree of stability"> maximum degree of stability</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20degree%20of%20stability" title=" robust degree of stability"> robust degree of stability</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20oscillation" title=" robust oscillation"> robust oscillation</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20accuracy" title=" system accuracy "> system accuracy </a> </p> <a href="https://publications.waset.org/abstracts/2551/synthesis-of-the-robust-regulators-on-the-basis-of-the-criterion-of-the-maximum-stability-degree" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2551.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">302</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1526</span> Methods of Variance Estimation in Two-Phase Sampling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Raghunath%20Arnab">Raghunath Arnab</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The two-phase sampling which is also known as double sampling was introduced in 1938. In two-phase sampling, samples are selected in phases. In the first phase, a relatively large sample of size is selected by some suitable sampling design and only information on the auxiliary variable is collected. During the second phase, a sample of size is selected either from, the sample selected in the first phase or from the entire population by using a suitable sampling design and information regarding the study and auxiliary variable is collected. Evidently, two phase sampling is useful if the auxiliary information is relatively easy and cheaper to collect than the study variable as well as if the strength of the relationship between the variables and is high. If the sample is selected in more than two phases, the resulting sampling design is called a multi-phase sampling. In this article we will consider how one can use data collected at the first phase sampling at the stages of estimation of the parameter, stratification, selection of sample and their combinations in the second phase in a unified setup applicable to any sampling design and wider classes of estimators. The problem of the estimation of variance will also be considered. The variance of estimator is essential for estimating precision of the survey estimates, calculation of confidence intervals, determination of the optimal sample sizes and for testing of hypotheses amongst others. Although, the variance is a non-negative quantity but its estimators may not be non-negative. If the estimator of variance is negative, then it cannot be used for estimation of confidence intervals, testing of hypothesis or measure of sampling error. The non-negativity properties of the variance estimators will also be studied in details. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=auxiliary%20information" title="auxiliary information">auxiliary information</a>, <a href="https://publications.waset.org/abstracts/search?q=two-phase%20sampling" title=" two-phase sampling"> two-phase sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=varying%20probability%20sampling" title=" varying probability sampling"> varying probability sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=unbiased%20estimators" title=" unbiased estimators"> unbiased estimators</a> </p> <a href="https://publications.waset.org/abstracts/36087/methods-of-variance-estimation-in-two-phase-sampling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36087.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">588</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1525</span> Refined Procedures for Second Order Asymptotic Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gubhinder%20Kundhi">Gubhinder Kundhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20Rilstone"> Paul Rilstone</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=edgeworth%20expansions" title="edgeworth expansions">edgeworth expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20order%20asymptotics" title=" higher order asymptotics"> higher order asymptotics</a>, <a href="https://publications.waset.org/abstracts/search?q=saddlepoint%20expansions" title=" saddlepoint expansions"> saddlepoint expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20instruments" title=" weak instruments"> weak instruments</a> </p> <a href="https://publications.waset.org/abstracts/68155/refined-procedures-for-second-order-asymptotic-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/68155.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">277</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1524</span> Robust ANOVA: An Illustrative Study in Horticultural Crop Research</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dinesh%20Inamadar">Dinesh Inamadar</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Venugopalan"> R. Venugopalan</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Padmini"> K. Padmini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An attempt has been made in the present communication to elucidate the efficacy of robust ANOVA methods to analyze horticultural field experimental data in the presence of outliers. Results obtained fortify the use of robust ANOVA methods as there was substantiate reduction in error mean square, and hence the probability of committing Type I error, as compared to the regular approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=outliers" title="outliers">outliers</a>, <a href="https://publications.waset.org/abstracts/search?q=robust%20ANOVA" title=" robust ANOVA"> robust ANOVA</a>, <a href="https://publications.waset.org/abstracts/search?q=horticulture" title=" horticulture"> horticulture</a>, <a href="https://publications.waset.org/abstracts/search?q=cook%20distance" title=" cook distance"> cook distance</a>, <a href="https://publications.waset.org/abstracts/search?q=type%20I%20error" title=" type I error"> type I error</a> </p> <a href="https://publications.waset.org/abstracts/21320/robust-anova-an-illustrative-study-in-horticultural-crop-research" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21320.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">390</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1523</span> Fault Diagnosis of Nonlinear Systems Using Dynamic Neural Networks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20Sobhani-Tehrani">E. Sobhani-Tehrani</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Khorasani"> K. Khorasani</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20Meskin"> N. Meskin </a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a novel integrated hybrid approach for fault diagnosis (FD) of nonlinear systems. Unlike most FD techniques, the proposed solution simultaneously accomplishes fault detection, isolation, and identification (FDII) within a unified diagnostic module. At the core of this solution is a bank of adaptive neural parameter estimators (NPE) associated with a set of single-parameter fault models. The NPEs continuously estimate unknown fault parameters (FP) that are indicators of faults in the system. Two NPE structures including series-parallel and parallel are developed with their exclusive set of desirable attributes. The parallel scheme is extremely robust to measurement noise and possesses a simpler, yet more solid, fault isolation logic. On the contrary, the series-parallel scheme displays short FD delays and is robust to closed-loop system transients due to changes in control commands. Finally, a fault tolerant observer (FTO) is designed to extend the capability of the NPEs to systems with partial-state measurement. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20fault%20diagnosis" title="hybrid fault diagnosis">hybrid fault diagnosis</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamic%20neural%20networks" title=" dynamic neural networks"> dynamic neural networks</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20systems" title=" nonlinear systems"> nonlinear systems</a>, <a href="https://publications.waset.org/abstracts/search?q=fault%20tolerant%20observer" title=" fault tolerant observer"> fault tolerant observer</a> </p> <a href="https://publications.waset.org/abstracts/23088/fault-diagnosis-of-nonlinear-systems-using-dynamic-neural-networks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23088.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">401</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1522</span> Parameters Estimation of Power Function Distribution Based on Selective Order Statistics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Moh%27d%20Alodat">Moh'd Alodat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fisher%20information" title="fisher information">fisher information</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20likelihood%20estimator" title=" maximum likelihood estimator"> maximum likelihood estimator</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20function%20distribution" title=" power function distribution"> power function distribution</a>, <a href="https://publications.waset.org/abstracts/search?q=ranked%20set%20sampling" title=" ranked set sampling"> ranked set sampling</a>, <a href="https://publications.waset.org/abstracts/search?q=selective%20order%20statistics%20sampling" title=" selective order statistics sampling"> selective order statistics sampling</a> </p> <a href="https://publications.waset.org/abstracts/40094/parameters-estimation-of-power-function-distribution-based-on-selective-order-statistics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40094.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">464</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1521</span> Bias-Corrected Estimation Methods for Receiver Operating Characteristic Surface</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khanh%20To%20Duc">Khanh To Duc</a>, <a href="https://publications.waset.org/abstracts/search?q=Monica%20Chiogna"> Monica Chiogna</a>, <a href="https://publications.waset.org/abstracts/search?q=Gianfranco%20Adimari"> Gianfranco Adimari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With three diagnostic categories, assessment of the performance of diagnostic tests is achieved by the analysis of the receiver operating characteristic (ROC) surface, which generalizes the ROC curve for binary diagnostic outcomes. The volume under the ROC surface (VUS) is a summary index usually employed for measuring the overall diagnostic accuracy. When the true disease status can be exactly assessed by means of a gold standard (GS) test, unbiased nonparametric estimators of the ROC surface and VUS are easily obtained. In practice, unfortunately, disease status verification via the GS test could be unavailable for all study subjects, due to the expensiveness or invasiveness of the GS test. Thus, often only a subset of patients undergoes disease verification. Statistical evaluations of diagnostic accuracy based only on data from subjects with verified disease status are typically biased. This bias is known as verification bias. Here, we consider the problem of correcting for verification bias when continuous diagnostic tests for three-class disease status are considered. We assume that selection for disease verification does not depend on disease status, given test results and other observed covariates, i.e., we assume that the true disease status, when missing, is missing at random. Under this assumption, we discuss several solutions for ROC surface analysis based on imputation and re-weighting methods. In particular, verification bias-corrected estimators of the ROC surface and of VUS are proposed, namely, full imputation, mean score imputation, inverse probability weighting and semiparametric efficient estimators. Consistency and asymptotic normality of the proposed estimators are established, and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations using real datasets are also given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=imputation" title="imputation">imputation</a>, <a href="https://publications.waset.org/abstracts/search?q=missing%20at%20random" title=" missing at random"> missing at random</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20probability%20weighting" title=" inverse probability weighting"> inverse probability weighting</a>, <a href="https://publications.waset.org/abstracts/search?q=ROC%20surface%20analysis" title=" ROC surface analysis"> ROC surface analysis</a> </p> <a href="https://publications.waset.org/abstracts/51883/bias-corrected-estimation-methods-for-receiver-operating-characteristic-surface" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/51883.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">416</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=robust%20estimators&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=robust%20estimators&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=robust%20estimators&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=robust%20estimators&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=robust%20estimators&page=6">6</a></li> <li class="page-item"><a class="page-link" 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