Asymptotic properties and information criteria for misspecified generalized linear mixed models

• 成果类型: Article
• 署名作者: Yu, Dalei; Zhang, Xinyu; Yau, Kelvin K. W.
• 署名单位: Yunnan University of Finance & Economics; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; City University of Hong Kong
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12270
• 发表日期: 2018
• 页码: 817-836
• 关键词: conditional akaike information; maximum-likelihood-estimation; inference; selection; regression

摘要

The problem of misspecification poses challenges in model selection. The paper studies the asymptotic properties of estimators for generalized linear mixed models with misspecification under the framework of conditional Kullback-Leibler divergence. A conditional generalized information criterion is introduced, and a model selection procedure is proposed by minimizing the criterion. We prove that the model selection procedure proposed is asymptotically loss efficient when all the candidate models are misspecified. The model selection consistency of the model selection procedure is also established when the true data-generating procedure lies within the set of candidate models. Simulation experiments confirm the effectiveness of the method proposed. The use of the criterion for model selection is illustrated through an analysis of the European Currency Opinion Survey data.