Empirical Likelihood Based Inferences for Partially Linear Models with Missing Covariates.

This paper considers statistical inference for partially linear models Y = X(T)mu + nu(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 nu(z). The resulting statistics are shown to be asymptotically chi-squared distributed. Finite sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a data set from an AIDS clinical trial.