Law of iterated logarithm and model selection consistency for generalized linear models with independent and dependent responses  

作　　者：Xiaowei YANG Shuang SONG Huiming ZHANG 

机构地区：[1]School of Mathematics and Statistics,Chaohu University,Chaohu,Hefei,238024,China [2]Center for Statistical Science,Tsinghua University,Beijing,100084,China [3]Department of Industrial Engineering,Tsinghua University,Beijing,100084,China [4]Department of Mathematics,University of Macao,Taipa Macao,China [5]UMacao Zhuhai Research Institute,Zhuhai,519000,China

出　　处：《Frontiers of Mathematics in China》2021年第3期825-856,共32页中国高等学校学术文摘·数学（英文）

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.

关 键 词：Generalized linear models(GLMs) weighted scores method non-natural link function model selection CONSISTENCY weakly dependent 

分 类 号：O17[理学—数学]