Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses
作者机构：School of Mathematics and StatisticsChaohu UniversityChaohuHefei238024China Center for Statistical ScienceTsinghua UniversityBeijing100084China Department of Industrial EngineeringTsinghua UniversityBeijing100084China Department of MathematicsUniversity of MacaoTaipa MacaoChina UMacao Zhuhai Research InstituteZhuhai519000China
出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)
年 卷 期：2021年第16卷第3期
页 面：825-856页
核心收录：
基 金：General Research Project of Chaohu University [XLY-201906] Chaohu University Applied Curriculum Development Project [ch19yykc21] University of Macau under UM Macao Talent Programme [UMMTP-2020-01] National Natural Science Foundation of China [11701109, 11901124] Guangxi Science Foundation [2018GXNSFAA138164]
主 题：Generalized linear models(GLMs) weighted scores method non-natural link function model selection consistency weakly dependent
摘 要：We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent (ρ-mixing) responses under mild conditions. The LIL is useful to derive the asymptotic bounds for the discrepancy between the empirical process of the log-likelihood function and the true log-likelihood. The strong consistency of some penalized likelihood-based model selection criteria can be shown as an application of the LIL. Under some regularity conditions, the model selection criterion will be helpful to select the simplest correct model almost surely when the penalty term increases with the model dimension, and the penalty term has an order higher than O(log log n) but lower than O(n). Simulation studies are implemented to verify the selection consistency of Bayesian information criterion.
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