Asymptotic Properties and Information Criteria for Misspecified Generalized Linear Mixed Models
研究了误设定下广义线性混合模型估计量的渐近性质，提出条件广义信息准则用于模型选择，并证明其在候选模型均误设时渐近损失有效，在真实模型包含于候选集时具有一致性。
Summary 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.