On the asymptotic behavior of the deficiency of some statist

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The purpose of this paper is to present some means for the comparison of the quality of estimators constructed from samples with random sizes with that of estimators constructed from samples with non-random sizes. As this means it is proposed to use the deficiency. It can be an illustrative characteristic of a possible loss of the accuracy of statistical inference if a random-size-sample is erroneously regarded as a sample with non-random size. It is heuristically shown that if the asymptotic distribution of the sample size normalized by its expectation is not degenerate, then the deficiency of a statistic constructed from a sample with random size whose expectation equals n with respect to the same statistic constructed as if the sample size was non-random and equal to n, grows almost linearly as n grows. A non-trivial behavior of the deficiency is possible only if the random sample size is asymptotically degenerate. This is the case considered in the paper where the deficiencies of statistics constructed from samples whose sizes have the Poisson, binomial and special three-point distributions, respectively, are considered. Some basic results dealing with some properties of estimators based on the samples with random sizes are also presented."> <meta name="citation_abstract_html_url" content="https://portuguese.alliedacademies.org/abstract/on-the-asymptotic-behavior-of-the-deficiency-of-some-statistical-estimators-basedrnon-samples-with-random-sizes-10902.html"> <link rel="shortcut icon" href="https://portuguese.alliedacademies.org/images/favicon.ico"/> <meta http-equiv="Content-Language" content="pt"> <link rel="canonical" href="https://portuguese.alliedacademies.org/abstract/on-the-asymptotic-behavior-of-the-deficiency-of-some-statistical-estimators-basedrnon-samples-with-random-sizes-10902.html"> <meta name="google-site-verification" content="G0zWsFYXLDgmFB8Gp4R_kyxwZFX83ob15xHbGLCxjpw" /> <link rel="alternate" href="https://portuguese.alliedacademies.org/abstract/on-the-asymptotic-behavior-of-the-deficiency-of-some-statistical-estimators-basedrnon-samples-with-random-sizes-10902.html" 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justify-content-between"> <div class="col-12 col-sm-12"> <h1 class="text-danger mb-0 font-size-26 fweight-500">Revista de Matemática Aplicada e Aplicações Estatísticas</h1> </div> </div> </div> </section> </header> <section class="py-4"> <div class="container"> <div class="row"> <main class="col-xs-12 col-sm-9 order-sm-12"> <div class="card border-5 rounded-0"> <div class="card-body"> <h2 class="border-bottom-1 brd-grey-500 text-danger d-flex w-100 justify-content-between align-items-center font-size-24 fweight-400">Abstrato</h2> <h1 class="font-size-20">On the asymptotic behavior of the deficiency of some statistical estimators based on samples with random sizes</h1> <p><i class="fas fa-user"></i> Bening VE </p> <p><p>Due to the stochastic character of the intensities of information flows in high performance information systems, the size of data available for the statistical analysis can be often regarded as random. The purpose of this paper is to present some means for the comparison of the quality of estimators constructed from samples with random sizes with that of estimators constructed from samples with non-random sizes. As this means it is proposed to use the deficiency. It can be an illustrative characteristic of a possible loss of the accuracy of statistical inference if a random-size-sample is erroneously regarded as a sample with non-random size. It is heuristically shown that if the asymptotic distribution of the sample size normalized by its expectation is not degenerate, then the deficiency of a statistic constructed from a sample with random size whose expectation equals n with respect to the same statistic constructed as if the sample size was non-random and equal to n, grows almost linearly as n grows. A non-trivial behavior of the deficiency is possible only if the random sample size is asymptotically degenerate. This is the case considered in the paper where the deficiencies of statistics constructed from samples whose sizes have the Poisson, binomial and special three-point distributions, respectively, are considered. Some basic results dealing with some properties of estimators based on the samples with random sizes are also presented.</p></p> <div class="alert alert-info text-left"><b>Isen莽茫o de responsabilidade:</b> Este resumo foi traduzido usando ferramentas de intelig锚ncia artificial e ainda n茫o foi revisado ou verificado.</div> <ul class="list-inline text-center"> <li class="list-inline-item"> <a title="Clique aqui" target="_blank" href="https://www.facebook.com/sharer.php?u=https://portuguese.alliedacademies.org/abstract/on-the-asymptotic-behavior-of-the-deficiency-of-some-statistical-estimators-basedrnon-samples-with-random-sizes-10902.html" rel="noopener" class="white" target="_blank"> <i class="bg-facebook theme-icons-sm fab fa-facebook-f"></i></a> </li> <li class="list-inline-item"> <a title="Clique aqui" target="_blank" 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On the asymptotic behavior of the deficiency of some statist | 10902