Optimal Model Averaging Estimation for Generalized Linear Models and Generalized Linear Mixed-Effects Models

ABSTRACT

Considering model averaging estimation in generalized linear models, we propose a weight choice criterion based on the Kullback–Leibler (KL) loss with a penalty term. This criterion is different from that for continuous observations in principle, but reduces to the Mallows criterion in the situation. We prove that the corresponding model averaging estimator is asymptotically optimal under certain assumptions. We further extend our concern to the generalized linear mixed-effects model framework and establish associated theory. Numerical experiments illustrate that the proposed method is promising.

KEYWORDS:

• Asymptotic optimality
• Kullback–Leibler loss
• Misspecification
• Penalized generalized weighted least squares (PGWLS)
• Prediction accuracy

Acknowledgments

The work of Zhang was performed during his visit to Prof. Raymond J. Carroll at Texas A&M University, whose support is gratefully appreciated. The authors thank the co-editors, an associate editor and three referees for their constructive suggestions and comments that have substantially improved an earlier version of this article.

Funding

Zhang's work was partially supported by National Natural Science Foundation of China (NNSFC, Grant nos. 71522004, 11471324 and 11271355). Yu's work was partially supported by NNSFC (Grant no. 11301463). Zou's work was partially supported by NNSFC (Grant no. 11331011) and the Beijing High-level Talents Program. Liang's work was partially supported by NSF grants DMS-1440121 and DMS-1418042, and Award Number 11529101, made by National Natural Science Foundation of China.