Jackknife empirical likelihood for the error variance in linear models

ABSTRACT

Variance estimation is a fundamental yet important problem in statistical modelling. In this paper, we propose jackknife empirical likelihood (JEL) methods for the error variance in a linear regression model. We prove that the JEL ratio converges to the standard chi-squared distribution. The asymptotic chi-squared properties for the adjusted JEL and extended JEL estimators are also established. Extensive simulation studies to compare the new JEL methods with the standard method in terms of coverage probability and interval length are conducted, and the simulation results show that our proposed JEL methods perform better than the standard method. We also illustrate the proposed methods using two real data sets.

KEYWORDS:

• Confidence interval
• empirical likelihood
• error variance
• jackknife empirical likelihood
• linear regression

Acknowledgements

The authors would like to thank two referees, an associate editor and editor-in-chief Professor Irène Gijbels for their helpful comments, which lead to a significant improvement in the previous version of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Zhouping Li was supported by the National Natural Science Foundation of China [11201207, 11571154]. The research of Yichuan Zhao is partially supported by an NSF Grant [DMS-1406163] and a National Security Agency Grant [H98230-12-1-0209].