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

• 成果类型: Article
• 署名作者: Zhang, Xinyu; Yu, Dalei; Zou, Guohua; Liang, Hua
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Yunnan University of Finance & Economics
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1115762
• 发表日期: 2016
• 页码: 1775-1790
• 关键词: focused information criterion; conditional inference; regression; selection

摘要

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.