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

Abstract

Summary This paper considers statistical inference for partially linear models Y = X ⊤ β +ν( Z ) +ɛ when the linear covariate X is missing with missing probability π depending upon ( Y , Z ). We propose empirical likelihood‐based statistics to construct confidence regions for β and ν( 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.