Bayesian empirical likelihood inference for the mean absolute deviation

Abstract

The mean absolute deviation (MAD) is a direct measure of the dispersion of a random variable about its mean. In this paper, the empirical likelihood (EL) and the adjusted EL methods for the MAD are proposed. The Bayesian empirical likelihood, the Bayesian adjusted empirical likelihood, the Bayesian jackknife empirical likelihood and the Bayesian adjusted jackknife empirical likelihood methods are used to construct credible intervals for the MAD. Simulation results show that the proposed EL method performs better than the JEL in Zhao et al. [Jackknife empirical likelihood inference for the mean absolute deviation. Comput Stat Data Anal. 2015;91:92–101], and the proper prior information improves coverage rates of confidence/credible intervals. Two real datasets are used to illustrate the new procedures.

Keywords:

• Adjusted empirical likelihood
• Bayesian empirical likelihood
• Bayesian jackknife empirical likelihood
• empirical likelihood
• mean absolute deviation

Acknowledgments

The authors thank the Editor-in-Chief, Professor Alexander Meister, the Associate Editor, and the two reviewers for their helpful comments, which improved the quality of the revision substantially. The authors are grateful to Dr. Xin Qi for the help in the verification of one result in the revision.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

Dr Hongyan Jiang would like to acknowledge the support from National Statistical Research program of China [grant number 2021-LY025] and the Natural Science Foundation of Huaiyin Institute of Technology [grant number ♯ 21HGZ013]. Dr Yichuan Zhao would like to thank the support from NSF [grant number DMS-2006304], NSF [grant number DMS-2317533] and the Simons Foundation [grant number ♯ 638679].