Empirical likelihood for partially linear models with missing responses at random

Abstract

Suppose that we have a partially linear model Yi=X′iβ+g(Ti)+εi with E(ε|X, T)=0, where {Xi, Ti, i=1, …, n} are random and observed completely, and {Yi, i=1, …, n} are missing at random (MAR). Empirical likelihood (EL) ratio statistics for the regression coefficient β and the nonparametric function g(t0) for fixed t0∈(0, 1) are constructed based on the inverse probability weighted imputation approach, which asymptotically have χ2-type distributions. These results are used to obtain EL-based confidence regions for β and g(t0). Results of a simulation study on the finite sample performance of EL-based confidence regions are presented.