Optimal Weight Choice for Frequentist Model Average Estimators

doi:10.1198/jasa.2011.tm09478

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	Optimal Weight Choice for Frequentist Model Average Estimators
	Liang, Hua 1; Zou, Guohua 2; Wan, Alan T. K.3; Zhang, Xinyu2
	2011-09-01
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	106 期号:495 页码:1053-1066
摘要	There has been increasing interest recently in model averaging within the frequentist paradigm. The main benefit of model averaging over model selection is that it incorporates rather than ignores the uncertainty inherent in the model selection process. One of the most important, yet challenging, aspects of model averaging is how to optimally combine estimates from different models. In this work, we suggest a procedure of weight choice for frequentist model average estimators that exhibits optimality properties with respect to the estimator's mean squared error (MSE). As a basis for demonstrating our idea, we consider averaging over a sequence of linear regression models. Building on this base, we develop a model weighting mechanism that involves minimizing the trace of an unbiased estimator of the model average estimator's MSE. We further obtain results that reflect the finite sample as well as asymptotic optimality of the proposed mechanism. A Monte Carlo study based on simulated and real data evaluates and compares the finite sample properties of this mechanism with those of existing methods. The extension of the proposed weight selection scheme to general likelihood models is also considered. This article has supplementary material online.
关键词	Asymptotic optimality Finite sample properties Mallows criterion Smoothed AIC Smoothed BIC Unbiased MSE estimate
DOI	10.1198/jasa.2011.tm09478
语种	英语
资助项目	NIH/NIADID[AI59773] ; NSF[DMS 0806097] ; NSF[DMS-1007167] ; National Natural Science Foundation of China[70625004] ; National Natural Science Foundation of China[10721101] ; Hong Kong Research Grant Council[GRF 102709]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000296224200031
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/12023
专题	系统科学研究所
通讯作者	Liang, Hua
作者单位	1.Univ Rochester, Med Ctr, Dept Biostat & Computat Biol, Rochester, NY 14642 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.City Univ Hong Kong, Dept Management Sci, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Liang, Hua,Zou, Guohua,Wan, Alan T. K.,et al. Optimal Weight Choice for Frequentist Model Average Estimators[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2011,106(495):1053-1066.
APA	Liang, Hua,Zou, Guohua,Wan, Alan T. K.,&Zhang, Xinyu.(2011).Optimal Weight Choice for Frequentist Model Average Estimators.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,106(495),1053-1066.
MLA	Liang, Hua,et al."Optimal Weight Choice for Frequentist Model Average Estimators".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 106.495(2011):1053-1066.