Semiparametric model-based inference in the presence of missing responses

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 χ-super-2 and scaled χ-super-2, respectively. Copyright 2008, Oxford University Press.