Empirical Likelihood for Semiparametric Varying-Coefficient Heteroscedastic Partially Linear Errors-in-Variables Models

Abstract

The purpose of this article is to use the empirical likelihood method to study construction of the confidence region for the parameter of interest in semiparametric varying-coefficient heteroscedastic partially linear errors-in-variables models. When the variance functions of the errors are known or unknown, we propose the empirical log-likelihood ratio statistics for the parameter of interest. For each case, a nonparametric version of Wilks’ theorem is derived. The results are then used to construct confidence regions of the parameter. A simulation study is carried out to assess the performance of the empirical likelihood method.

Keywords:

• Confidence regions/intervals
• Empirical likelihood
• Heteroscedastic
• Partially linear errors-in-variables model
• Varying-coefficient model

Mathematics Subject Classification:

• 62G15
• 62E20

Acknowledgments

The authors are grateful to the Editor and referee for their valuable comments with our article. This research was supported by the National Natural Science Foundation of China (71171003, 11226218, 11101114), Provincial Natural Science Research Project of Anhui Colleges (KJ2011A032, KJ2011A032), Anhui Provincial Natural Science Foundation (1208085QA04, 10040606Q03), the Fundamental Research Funds for the Central Universities (30920130111015), and the Postdoctoral Positions of Anhui Normal University.