Semiparametric model-based inference in the presence of missing responses

We consider a semiparametric model that parameterizes the conditionaldensity of the response, given covariates, but allows the marginaldistribution of the covariates to be completely arbitrary. Responsesmay be missing. A likelihood-based imputation estimator anda semi-empirical-likelihood-based estimator for the parametervector describing the conditional density are defined and provedto be asymptotically normal. Semi-empirical loglikelihood functionsfor the parameter vector and the response mean are derived.It is shown that the two semi-empirical loglikelihood functionsare distributed asymptotically as weighted ² and scaled ², respectively.