Empirical Likelihood Confidence Region for the Parameter in a Partially Linear Errors-in-Variables Model

Abstract

In this article, a partially linear errors-in-variables model is considered, and empirical log-likelihood ratio statistic for the unknown parameter in the model is suggested. It is proved that the proposed statistic is asymptotically standard chi-square distribution under some suitable conditions, and hence it can be used to construct the confidence region of the parameter. A simulation study indicates that, in terms of coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the least-squares method.

Keywords:

• Chi-square distribution
• Confidence region
• Coverage probability
• Eempirical likelihood
• Partially linear errors-in-variables model

Mathematics Subject Classification:

• Primary 62J02
• Secondary 62E20

Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant 10571008), the Natural Science Foundation of Beijing (Grant 1072004), Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality and the Basic Research and Frontier Technology Foundation of Henan (Grant 072300410090). The authors would like to thank the editor, the associate editor, and the referees for helpful comments, which helped to improve an earlier version of the article.