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.
Publié le : 1998-06-14
Classification:
Generalized linear models,
kernel regression,
local linear smoother,
measurement error,
missing at random,
quasilikelihood functions,
62G07,
62G20
@article{1024691087,
author = {Wang, C. Y. and Wang, Suojin and Gutierrez, Roberto G. and Carroll, R. J.},
title = {Local linear regression for generalized linear models with missing
data},
journal = {Ann. Statist.},
volume = {26},
number = {3},
year = {1998},
pages = { 1028-1050},
language = {en},
url = {http://dml.mathdoc.fr/item/1024691087}
}
Wang, C. Y.; Wang, Suojin; Gutierrez, Roberto G.; Carroll, R. J. Local linear regression for generalized linear models with missing
data. Ann. Statist., Tome 26 (1998) no. 3, pp. 1028-1050. http://gdmltest.u-ga.fr/item/1024691087/