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.

Keywords:

• partially linear model
• heteroscedasticity test
• missing at random
• empirical likelihood ratio

AMS Subject Classification :

• 62H15
• 62N99

Acknowledgements

The authors thank Profession Yijun Zuo for his great help. This paper was partially supported by Natural Science Foundation Project of CQ CSTC (No. 2009BB8221) and the National Natural Science of China (No. 10871217). The authors thank the editor, the associate editor and two anonymous reviewers, whose helpful comments greatly improved the presentation of this paper.