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Korean Stat. Soc.</a> <a href="/?q=in%3A481072" title="Articles in this Issue">49, No. 4, 1148-1172 (2020)</a>. </div> <div class="abstract">Summary: This paper investigates estimation of semiparametric varying-coefficient spatial autoregressive models in which the dependent variable is missing at random. An inverse propensity score weighted sieve two-stage least squares (S-2SLS) estimation with imputation is proposed. The proposed estimators are shown to be consistent, no matter the initial value is taken as the naive S-2SLS estimate or the naive nonlinear least squares estimate, and the asymptotic distribution of the latter is also derived. Simulation studies are carried out to investigate the performance of the proposed estimator. The method is finally exemplified with one real data set on Boston housing prices.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7514875">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M10" title="MSC2020">62M10</a> </td> <td class="space"> Time series, auto-correlation, regression, etc. in statistics (GARCH) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62D10" title="MSC2020">62D10</a> </td> <td class="space"> Missing data </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62F12" title="MSC2020">62F12</a> </td> <td class="space"> Asymptotic properties of parametric estimators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62M30" title="MSC2020">62M30</a> </td> <td class="space"> Inference from spatial processes </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P20" title="MSC2020">62P20</a> </td> <td class="space"> Applications of statistics to economics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asemiparametric+model">semiparametric model</a>; <a href="/?q=ut%3Aspatial+data">spatial data</a>; <a href="/?q=ut%3Apropensity+score">propensity score</a>; <a href="/?q=ut%3Amissing+data">missing data</a>; <a href="/?q=ut%3Ainstrumental+variable">instrumental variable</a></div> <div class="software"> <h3>Software:</h3><a href="/software/7176">Arc_Mat</a>; <a href="/software/4578">spdep</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;"> <!-- alert for connection errors etc --> </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1485.62126" data-ciurl="/ci/07514875" data-biburl="/bibtex/07514875.bib" data-amsurl="/amsrefs/07514875.bib" data-xmlurl="/xml/07514875.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07514875.pdf" title="Zbl 1485.62126 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s42952-019-00048-2" aria-label="DOI for “Estimation of semiparametric varying-coefficient spatial autoregressive models with missing in the dependent variable”" title="10.1007/s42952-019-00048-2">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Anselin, L., Spatial econometrics: Methods and models (1988), Bost: Kluwer, Bost · <a href="https://doi.org/10.1007/978-94-015-7799-1" class="nowrap">doi:10.1007/978-94-015-7799-1</a></td> </tr><tr> <td>[2]</td> <td class="space">Ai, C.; Chen, X., Efficient estimation of models with conditional moment restrictions containing unknown functions, Econometrica, 71, 1795-1843 (2003) · <a href="/1154.62323" class="nowrap">Zbl 1154.62323</a> · <a href="https://doi.org/10.1111/1468-0262.00470" class="nowrap">doi:10.1111/1468-0262.00470</a></td> </tr><tr> <td>[3]</td> <td class="space">Ai, C.; Zhang, Y., Estimation of partially specified spatial panel data models with fixed-effects, Econometric Reviews, 36, 1-3, 6-22 (2017) · <a href="/1524.62561" class="nowrap">Zbl 1524.62561</a> · <a href="https://doi.org/10.1080/07474938.2015.1113641" class="nowrap">doi:10.1080/07474938.2015.1113641</a></td> </tr><tr> <td>[4]</td> <td class="space">Basile, R., Productivity polarization across regions in Europe: The role of nonlinearities and spatial dependence, Article International Regional Science Review, 32, 92-115 (2009) · <a href="https://doi.org/10.1177/0160017608326944" class="nowrap">doi:10.1177/0160017608326944</a></td> </tr><tr> <td>[5]</td> <td class="space">Bell, KP; Bockstael, NE, Applying the generalized-moment estimation approach to spatial problems involving microlevel data, Review of Economics and Statistics, 82, 72-82 (2000) · <a href="https://doi.org/10.1162/003465300558641" class="nowrap">doi:10.1162/003465300558641</a></td> </tr><tr> <td>[6]</td> <td class="space">Besley, T.; Case, AC, Incumbent behavior: Vote-seeking, tax-setting, and yardstick competition, The American Economic Review, 85, 25-45 (1995)</td> </tr><tr> <td>[7]</td> <td class="space">Bivand, R., (2017). spdep: Spatial dependence: Weighting schemes, statistics and models. http://CRAN.R-project.org/package=spdep. Accessed on 6 Nov 2017.</td> </tr><tr> <td>[8]</td> <td class="space">Case, AC, Spatial patterns in household demand, Econometrica, 59, 953-965 (1991) · <a href="https://doi.org/10.2307/2938168" class="nowrap">doi:10.2307/2938168</a></td> </tr><tr> <td>[9]</td> <td class="space">Cliff, A.; Ord, JK, Spatial autocorrelation (1973), London: Pion, London</td> </tr><tr> <td>[10]</td> <td class="space">Cheng, PE, Nonparametric estimation of mean functionals with data missing at random, Journal of the American Statistical Association, 89, 81-87 (1994) · <a href="/0800.62213" class="nowrap">Zbl 0800.62213</a> · <a href="https://doi.org/10.1080/01621459.1994.10476448" class="nowrap">doi:10.1080/01621459.1994.10476448</a></td> </tr><tr> <td>[11]</td> <td class="space">Cao, WH; Tsiatis, AA; Davidian, M., Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data, Biometrika, 96, 723-734 (2009) · <a href="/1170.62007" class="nowrap">Zbl 1170.62007</a> · <a href="https://doi.org/10.1093/biomet/asp033" class="nowrap">doi:10.1093/biomet/asp033</a></td> </tr><tr> <td>[12]</td> <td class="space">Davidson, R.; MacKinnon, JG, Econometric theory and methods (2004), New York: Oxford University Press, New York</td> </tr><tr> <td>[13]</td> <td class="space">Du, J.; Sun, XQ; Cao, RY; Zhang, ZZ, Statistical inference for partially linear additive spatial autoregressive models, Spatial Statistics, 25, 52-67 (2018) · <a href="https://doi.org/10.1016/j.spasta.2018.04.008" class="nowrap">doi:10.1016/j.spasta.2018.04.008</a></td> </tr><tr> <td>[14]</td> <td class="space">Fan, JQ; Huang, T., Profile likelihood inferences on semiparametric varying coefficient partially linear models, Bernoulli, 11, 1031-1057 (2005) · <a href="/1098.62077" class="nowrap">Zbl 1098.62077</a> · <a href="https://doi.org/10.3150/bj/1137421639" class="nowrap">doi:10.3150/bj/1137421639</a></td> </tr><tr> <td>[15]</td> <td class="space">Horvitz, DG; Thompson, DJ, A generalization of sampling without replacement from a finite universe, Journal of the American statistical Association, 47, 663-685 (1952) · <a href="/0047.38301" class="nowrap">Zbl 0047.38301</a> · <a href="https://doi.org/10.1080/01621459.1952.10483446" class="nowrap">doi:10.1080/01621459.1952.10483446</a></td> </tr><tr> <td>[16]</td> <td class="space">Healy, M.; Westmacott, M., Missing values in experiments analysed on automatic computers, Journal of the Royal Statistical Society, 5, 203-206 (1956)</td> </tr><tr> <td>[17]</td> <td class="space">Huang, J. Z., Wu, C. O., & Zhou, L. (2004). Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Statistica Sinica, 763-788. · <a href="/1073.62036" class="nowrap">Zbl 1073.62036</a></td> </tr><tr> <td>[18]</td> <td class="space">Kelejian, HH; Prucha, IR, A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbance, Journal of Real Estate Finance and Economics, 17, 99-121 (1998) · <a href="https://doi.org/10.1023/A:1007707430416" class="nowrap">doi:10.1023/A:1007707430416</a></td> </tr><tr> <td>[19]</td> <td class="space">Kelejian, HH; Prucha, IR, A generalized moments estimator for the autoregressive parameter in a spatial model, International Economic Review, 40, 509-533 (1999) · <a href="https://doi.org/10.1111/1468-2354.00027" class="nowrap">doi:10.1111/1468-2354.00027</a></td> </tr><tr> <td>[20]</td> <td class="space">Kelejian, HH; Prucha, IR, Spatial models with spatially lagged dependent variables and incomplete data, Journal of geographical systems, 12, 241-257 (2010) · <a href="https://doi.org/10.1007/s10109-010-0109-5" class="nowrap">doi:10.1007/s10109-010-0109-5</a></td> </tr><tr> <td>[21]</td> <td class="space">Imai, K.; Ratkovic, M., Covariate balancing propensity score, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 243-263 (2014) · <a href="/1411.62025" class="nowrap">Zbl 1411.62025</a> · <a href="https://doi.org/10.1111/rssb.12027" class="nowrap">doi:10.1111/rssb.12027</a></td> </tr><tr> <td>[22]</td> <td class="space">Little, Roderick J. A.; Rubin, Donald B., Statistical analysis with missing data (2002), Hoboken: Wiley, Hoboken · <a href="/1011.62004" class="nowrap">Zbl 1011.62004</a> · <a href="https://doi.org/10.1002/9781119013563" class="nowrap">doi:10.1002/9781119013563</a></td> </tr><tr> <td>[23]</td> <td class="space">Lee, L.; Liu, X.; Lin, X., Specification and estimation of social interaction models with network structures, Econometrics Journal, 13, 145-176 (2010) · <a href="/1217.91162" class="nowrap">Zbl 1217.91162</a> · <a href="https://doi.org/10.1111/j.1368-423X.2010.00310.x" class="nowrap">doi:10.1111/j.1368-423X.2010.00310.x</a></td> </tr><tr> <td>[24]</td> <td class="space">Lee, LF, Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances, Econometric Reviews, 22, 4, 307-335 (2003) · <a href="/1030.62069" class="nowrap">Zbl 1030.62069</a> · <a href="https://doi.org/10.1081/ETC-120025891" class="nowrap">doi:10.1081/ETC-120025891</a></td> </tr><tr> <td>[25]</td> <td class="space">Lee, LF, Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models, Econometrica, 72, 1899-1925 (2004) · <a href="/1142.62312" class="nowrap">Zbl 1142.62312</a> · <a href="https://doi.org/10.1111/j.1468-0262.2004.00558.x" class="nowrap">doi:10.1111/j.1468-0262.2004.00558.x</a></td> </tr><tr> <td>[26]</td> <td class="space">Lee, LF, GMM and 2SLS estimation of mixed regressive, spatial autoregressive models, Journal of Econometrics, 137, 489-514 (2007) · <a href="/1360.62476" class="nowrap">Zbl 1360.62476</a> · <a href="https://doi.org/10.1016/j.jeconom.2005.10.004" class="nowrap">doi:10.1016/j.jeconom.2005.10.004</a></td> </tr><tr> <td>[27]</td> <td class="space">LeSage, J.; Pace, RK, Introduction to spatial econometrics (2009), Boca Raton: Chapman and Hall/CRC, Boca Raton · <a href="/1163.91004" class="nowrap">Zbl 1163.91004</a> · <a href="https://doi.org/10.1201/9781420064254" class="nowrap">doi:10.1201/9781420064254</a></td> </tr><tr> <td>[28]</td> <td class="space">Luo, GW; Wu, MX, Variable selection for semiparametric varying-coefficient spatial autoregressive models with a diverging number of parameters, Communications in Statistics-Theory and Methods (2019) · <a href="/07530953" class="nowrap">Zbl 07530953</a> · <a href="https://doi.org/10.1080/03610926.2019.1659367" class="nowrap">doi:10.1080/03610926.2019.1659367</a></td> </tr><tr> <td>[29]</td> <td class="space">Luo, GW; Wu, MX, Statistical inference for semiparametric varying -coefficient spatial autoregressive models under restricted conditions, Communications in Statistics-Simulation and Computation (2019) · <a href="/07545863" class="nowrap">Zbl 07545863</a> · <a href="https://doi.org/10.1080/03610918.2019.1693595" class="nowrap">doi:10.1080/03610918.2019.1693595</a></td> </tr><tr> <td>[30]</td> <td class="space">Newey, W.; McFadden, D.; Engle, RF; McFadden, DL, Large sample estimation and hypothesis testing, Handbook of econometrics, 2111-2224 (1994), Amsterdam: North-Holland, Amsterdam</td> </tr><tr> <td>[31]</td> <td class="space">Ord, K., Estimation methods for models of spatial interaction, Journal of the American Statistical Association, 70, 349, 120-126 (1975) · <a href="/0313.62063" class="nowrap">Zbl 0313.62063</a> · <a href="https://doi.org/10.1080/01621459.1975.10480272" class="nowrap">doi:10.1080/01621459.1975.10480272</a></td> </tr><tr> <td>[32]</td> <td class="space">Robins, JM; Rotnitzky, A.; Zhao, LP, Estimation of regression coefficients when some regressors are not always observed, Journal of the American Statistical Association, 89, 846-866 (1994) · <a href="/0815.62043" class="nowrap">Zbl 0815.62043</a> · <a href="https://doi.org/10.1080/01621459.1994.10476818" class="nowrap">doi:10.1080/01621459.1994.10476818</a></td> </tr><tr> <td>[33]</td> <td class="space">Schumaker, LL, Spline functions (1981), New York: Wiley, New York · <a href="/0449.41004" class="nowrap">Zbl 0449.41004</a></td> </tr><tr> <td>[34]</td> <td class="space">Su, LJ; Jin, SN, Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models, Journal of Econometrics, 157, 18-33 (2010) · <a href="/1431.62420" class="nowrap">Zbl 1431.62420</a> · <a href="https://doi.org/10.1016/j.jeconom.2009.10.033" class="nowrap">doi:10.1016/j.jeconom.2009.10.033</a></td> </tr><tr> <td>[35]</td> <td class="space">Su, LJ, Semiparametric GMM estimation of spatial autoregressive models, Journal of Econometrics, 167, 543-560 (2012) · <a href="/1441.62877" class="nowrap">Zbl 1441.62877</a> · <a href="https://doi.org/10.1016/j.jeconom.2011.09.034" class="nowrap">doi:10.1016/j.jeconom.2011.09.034</a></td> </tr><tr> <td>[36]</td> <td class="space">Wang, CY; Wang, S.; Gutierrez, RG; Carroll, RJ, Local linear regression for generalized linear models with missing data, Annals of Statistics, 26, 1028-1050 (1998) · <a href="/1073.62548" class="nowrap">Zbl 1073.62548</a> · <a href="https://doi.org/10.1214/aos/1024691087" class="nowrap">doi:10.1214/aos/1024691087</a></td> </tr><tr> <td>[37]</td> <td class="space">Wang, W.; Lee, LF, Estimation of spatial autoregressive models with randomly missing data in the dependent variable, The Econometrics Journal, 16, 73-102 (2013) · <a href="/1521.62186" class="nowrap">Zbl 1521.62186</a> · <a href="https://doi.org/10.1111/j.1368-423X.2012.00388.x" class="nowrap">doi:10.1111/j.1368-423X.2012.00388.x</a></td> </tr><tr> <td>[38]</td> <td class="space">Wang, Q.; Linton, O.; Härdle, W., Semiparametric regression analysis with missing response at random, Journal of the American Statistical Association, 99, 334-345 (2004) · <a href="/1117.62441" class="nowrap">Zbl 1117.62441</a> · <a href="https://doi.org/10.1198/016214504000000449" class="nowrap">doi:10.1198/016214504000000449</a></td> </tr><tr> <td>[39]</td> <td class="space">Yu, J.; de Jong, R.; Lee, LF, Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration, Journal of Econometrics, 167, 1, 16-37 (2012) · <a href="/1441.62908" class="nowrap">Zbl 1441.62908</a> · <a href="https://doi.org/10.1016/j.jeconom.2011.05.014" class="nowrap">doi:10.1016/j.jeconom.2011.05.014</a></td> </tr><tr> <td>[40]</td> <td class="space">Zhang, G.; Little, RJ, Extensions of the Penalized Spline of Propensity Prediction Method of Imputation, Biometrics, 65, 911-918 (2009) · <a href="/1172.62071" class="nowrap">Zbl 1172.62071</a> · <a href="https://doi.org/10.1111/j.1541-0420.2008.01155.x" class="nowrap">doi:10.1111/j.1541-0420.2008.01155.x</a></td> </tr><tr> <td>[41]</td> <td class="space">Zhang, YQ; Shen, DM, Estimation of semi-parametric varying-coefficient spatial panel data models with random-effects, Journal of Statistical Planning and Inference, 159, 64-80 (2015) · <a href="/1311.62164" class="nowrap">Zbl 1311.62164</a> · <a href="https://doi.org/10.1016/j.jspi.2014.11.001" class="nowrap">doi:10.1016/j.jspi.2014.11.001</a></td> </tr><tr> <td>[42]</td> <td class="space">Zhang, Y.; Sun, Y., Estimation of partially specified dynamic spatial panel data models with fixed-effects, Regional science and urban economics, 51, 37-46 (2015) · <a href="https://doi.org/10.1016/j.regsciurbeco.2015.01.003" class="nowrap">doi:10.1016/j.regsciurbeco.2015.01.003</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. 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