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Biometrika 2008 95(3):721-734; doi:10.1093/biomet/asn032
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© 2008 Biometrika Trust

Articles

Semiparametric model-based inference in the presence of missing responses

Qihua Wang and Pengjie Dai

Academy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 100080, China qhwang{at}amss.ac.cn jackdpj{at}yahoo.com.cn

Received for publication 1 June 2007. Revision received 1 January 2008.
  Abstract

We consider a semiparametric model that parameterizes the conditional density of the response, given covariates, but allows the marginal distribution of the covariates to be completely arbitrary. Responses may be missing. A likelihood-based imputation estimator and a semi-empirical-likelihood-based estimator for the parameter vector describing the conditional density are defined and proved to be asymptotically normal. Semi-empirical loglikelihood functions for the parameter vector and the response mean are derived. It is shown that the two semi-empirical loglikelihood functions are distributed asymptotically as weighted {chi}2 and scaled {chi}2, respectively.

Key Words: Asymptotic efficiency • Missing response • Multiple imputation • Semi-empirical likelihood • Auxiliary information • Asymptotic Normality


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