Testing heteroscedasticity in partially linear models with missing covariates

Abstract

The purpose of this paper is to investigate the underlying heteroscedasticity in a partially linear model with missing covariates by using the empirical likelihood method. Two new test statistics are proposed based on the inverse probability-weighted idea. Under the null hypothesis, the resulting test statistics are shown to have standard chi-squared distributions asymptotically. Simulation studies show that the proposed statistics behave well. An example of an AIDS clinical trial data set is also used for illustrating our methods.