Open Access
June 1998 Local linear regression for generalized linear models with missing data
R. J. Carroll, Roberto G. Gutierrez, C. Y. Wang, Suojin Wang
Ann. Statist. 26(3): 1028-1050 (June 1998). DOI: 10.1214/aos/1024691087


Fan, Heckman and Wand proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions. When the covariate variables are missing at random, we propose a weighted estimator based on the inverse selection probability weights. Distribution theory is derived when the selection probabilities are estimated nonparametrically. We show that the asymptotic variance of the resulting nonparametric estimator of the mean function in the main regression model is the same as that when the selection probabilities are known, while the biases are generally different. This is different from results in parametric problems, where it is known that estimating weights actually decreases asymptotic variance. To reconcile the difference between the parametric and nonparametric problems, we obtain a second-order variance result for the nonparametric case. We generalize this result to local estimating equations. Finite-sample performance is examined via simulation studies. The proposed method is demonstrated via an analysis of data from a case-control study.


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R. J. Carroll. Roberto G. Gutierrez. C. Y. Wang. Suojin Wang. "Local linear regression for generalized linear models with missing data." Ann. Statist. 26 (3) 1028 - 1050, June 1998.


Published: June 1998
First available in Project Euclid: 21 June 2002

zbMATH: 1073.62548
MathSciNet: MR1635438
Digital Object Identifier: 10.1214/aos/1024691087

Primary: 62G07
Secondary: 62G20

Keywords: generalized linear models , kernel regression , local linear smoother , measurement error , missing at random , quasilikelihood functions

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 3 • June 1998
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