Empirical Likelihood for a Heteroscedastic Partial Linear Errors-in-Variables Model

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 heteroscedastic partially linear errors-in-variables model with martingale difference errors. 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 region
• Empirical likelihood
• Heteroscedastic partial linear errors-in-variables model
• Local linear method
• Martingale difference error

Mathematics Subject Classification:

• 62G15
• 62E20

Acknowledgments

We thank the reviewers for their helpful comments, which greatly improved the presentation of the article. This research was supported by the National Natural Science Foundation of China (10871146, 71171003); the Young Teachers Science Research Foundation of Anhui Polytechnic University (2009YQ035); Provincial Natural Science Research Project of Anhui Colleges (KJ2011A032); Anhui Provincial Natural Science Foundation, Anhui Polytechnic University Foundation for Recruiting Talent (2011YQQ004); and Scientific research project of education department of Zhejiang Province (Y200906404) and China Post doctoral Science Foundation (2011M500622).