Model averaging for M-estimation

ABSTRACT

M-estimation is a widely used technique for robust statistical inference. In this paper, we study model selection and model averaging for M-estimation to simultaneously improve the coverage probability of confidence intervals of the parameters of interest and reduce the impact of heavy-tailed errors or outliers in the response. Under general conditions, we develop robust versions of the focused information criterion and a frequentist model average estimator for M-estimation, and we examine their theoretical properties. In addition, we carry out extensive simulation studies as well as two real examples to assess the performance of our new procedure, and find that the proposed method produces satisfactory results.

KEYWORDS:

• Model averaging estimators
• focused information criterion
• model selection
• model uncertainty

2008 MSC:

• 62J99
• 62F35

Acknowledgements

We would like to thank the referees and editors for their constructive and insightful comments and suggestions that greatly improved the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Du's work is supported by the National Natural Science Foundation of China (No. 11501018, No. 11571340), Program for Rixin Talents in Beijing University of Technology. Zhang's work is partly supported by the (No. 11271039), and Education Ministry Funds of China for Doctor Supervisors (20131103110027). Xie's work is supported by the Science and Technology Project of Beijing Municipal Education Commission (KM201710005032).