EMPIRICAL LIKELIHOOD-BASED INFERENCES FOR PARTIALLY LINEAR MODELS WITH MISSING COVARIATES

This paper considers statistical inference for partially linear models Y = X(inverted perpendicular) beta + v(Z) + epsilon when the linear covariate X is missing with missing probability pi depending upon (Y, Z). We propose empirical likelihood-based statistics to construct confidence regions for beta and v(z). The resulting empirical likelihood ratio statistics are shown to be asymptotically chi-squared-distributed. The finite-sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a dataset from an AIDS clinical trial.