Estimation in Partially Linear Single-Index Models with Missing Covariates
In this article, we consider a partially linear single-index model Y = g(Z τθ0) + X τβ0 + ϵ when the covariate X may be missing at random. We propose weighted estimators for the unknown parametric and nonparametric part by applying weighted estimating equations. We establish normality of the estimators of the parameters and asymptotic expansion for the estimator of the nonparametric part when the selection probabilities are unknown. Simulation studies are also conducted to illustrate the finite sample properties of these estimators.