zbMATH — the first resource for mathematics

Weighted least squares estimation with missing responses: an empirical likelihood approach. (English) Zbl 1336.62092
Summary: A heteroscedastic linear regression model is considered where responses are allowed to be missing at random. An estimator is constructed that matches the performance of the weighted least squares estimator without the knowledge of the conditional variance function. This is usually done by constructing an estimator of the variance function. Our estimator is a maximum empirical likelihood estimator based on an increasing number of estimated constraints and avoids estimating the variance function.

MSC:
 62F12 Asymptotic properties of parametric estimators 62G05 Nonparametric estimation 62J05 Linear regression; mixed models
Full Text:
References:
 [1] Carroll, R. J. (1982). Adapting for heteroscedasticity in linear models. Ann. Statist. 10 1224-1233. · Zbl 0571.62058 [2] Chamberlain, G. (1987). Asymptotic efficiency in estimation with conditional moment restrictions. J. Econometrics 34 305-334. · Zbl 0618.62040 [3] Chen, S.X., Peng, L. and Qin, Y.-L. (2009). Effects of data dimension on empirical likelihood. Biometrika 96 711-722. · Zbl 1170.62023 [4] Hjort, N.L., McKeague, I.W. and Van Keilegom, I. (2009). Extending the scope of empirical likelihood. Ann. Statist. 37 1079-1111. · Zbl 1160.62029 [5] Koul, H., Müller, U.U. and Schick, A. (2012). The transfer principle: a tool for complete case analysis. Ann. Statist. 60 3031-3047. · Zbl 1296.62040 [6] Little, R.J.A. and Rubin, D.B. (2002). Statistical Analysis with Missing Data. Second edition. Wiley Series in Probability and Statistics, Wiley, Hoboken. · Zbl 1011.62004 [7] Müller, H. G. and Stadtmüller, U. (1987). Estimation of heteroscedasticity in regression analysis. Ann. Statist. 15 610-625. · Zbl 0632.62040 [8] Müller, U.U. and Van Keilegom, I. (2012). Efficient parameter estimation in regression with missing responses. Electron. J. Statist. 6 1200-1219. · Zbl 1295.62022 [9] Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 237-249. · Zbl 0641.62032 [10] Owen, A. B. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18 90-120. · Zbl 0712.62040 [11] Owen, A.B. (2001). Empirical Likelihood . Chapman & Hall/CRC. · Zbl 0989.62019 [12] Peng, H. and Schick, A. (2012a). Empirical likelihood approach to goodness of fit testing. To appear in Bernoulli . · Zbl 1273.62103 [13] Peng, H. and Schick, A. (2012b). Maximum empirical likelihood estimation and related topics. Preprint available at . [14] Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. Ann. Statist. 22 300-325. · Zbl 0799.62049 [15] Robinson, P. M. (1987). Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55 875-891. · Zbl 0651.62107 [16] Schick, A. (1987). A note on the construction of asymptotically linear estimators. J. Statist. Plann. Inference 16 , 89-105. Correction (1989) 22 269-270. · Zbl 0634.62036 [17] Tsiatis, A.A. (2006). Semiparametric Theory and Missing Data. Springer Series in Statistics. Springer, New York. · Zbl 1105.62002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.