Empirical likelihood for partially linear models with missing responses at random

Abstract

Suppose that we have a partially linear model Y _i =X′ _i β+g(T _i )+ε _i with E(ε|X, T)=0, where {X _i , T _i , i=1, …, n} are random and observed completely, and {Y _i , i=1, …, n} are missing at random (MAR). Empirical likelihood (EL) ratio statistics for the regression coefficient β and the nonparametric function g(t ₀) for fixed t ₀∈(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(t ₀). Results of a simulation study on the finite sample performance of EL-based confidence regions are presented.

Keywords:

• partially linear model
• empirical likelihood
• missing at random
• confidence region

AMS 2000 Subject Classification :

• Primary 62G05
• Secondary 62E20

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (10971038), the Natural Science Foundation of Guangxi(2010 GXNSFA 013117) and the Program for Excellent Talents in Guangxi Higher Education Institutions. The authors are thankful to the referees for their constructive suggestions.