Biometrika Advance Access published online on February 28, 2007
Biometrika, doi:10.1093/biomet/asm010
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Partially linear models with missing response variables and error-prone covariates
Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, New York 14642, U.S.A.
Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A.
hliang{at}bst.rochester.edu
sjwang{at}stat.tamu.edu
carroll{at}stat.tamu.edu
Received for publication 1 October 2005.
Revision received 1 June 2006.
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Abstract |
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We consider partially linear models of the form Y = XTß + 
(Z) + 
when the response variable Y is sometimes missing with missingness probability 
depending on (X, Z), and the covariate X is measured with error, where (z) is an unspecified smooth function. The missingness structure is therefore missing not at random, rather than the usual missing at random. We propose a class of semiparametric estimators for the parameter of interest ß, as well as for the population mean E(Y). The resulting estimators are shown to be consistent and asymptotically normal under general assumptions. To construct a confidence region for ß, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. The proposed methods are applied to an AIDS clinical trial dataset. A simulation study is also reported.
Key Words: confidence region • empirical likelihood • estimating equation • measurement error • missing data • missing not at random • nonparametric regression • semiparametric estimation