Parsimonious Model Averaging With a Diverging Number of Parameters

doi:10.1080/01621459.2019.1604363

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	Parsimonious Model Averaging With a Diverging Number of Parameters
	Zhang, Xinyu1,2 ; Zou, Guohua 3; Liang, Hua 4; Carroll, Raymond J.5,6
	2019-06-18
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
页码	13
摘要	Model averaging generally provides better predictions than model selection, but the existing model averaging methods cannot lead to parsimonious models. Parsimony is an especially important property when the number of parameters is large. To achieve a parsimonious model averaging coefficient estimator, we suggest a novel criterion for choosing weights. Asymptotic properties are derived in two practical scenarios: (i) one or more correct models exist in the candidate model set and (ii) all candidate models are misspecified. Under the former scenario, it is proved that our method can put the weight one to the smallest correct model and the resulting model averaging estimators of coefficients have many zeros and thus lead to a parsimonious model. The asymptotic distribution of the estimators is also provided. Under the latter scenario, prediction is mainly focused on and we prove that the proposed procedure is asymptotically optimal in the sense that its squared prediction loss and risk are asymptotically identical to those of the best-but infeasible-model averaging estimator. Numerical analysis shows the promise of the proposed procedure over existing model averaging and selection methods.
关键词	Asymptotic optimality Frequentist model averaging Jackknife model averaging Mallows model averaging Parsimony
DOI	10.1080/01621459.2019.1604363
语种	英语
资助项目	National Natural Science Foundation of China (NNSFC)[71522004] ; National Natural Science Foundation of China (NNSFC)[11471324] ; National Natural Science Foundation of China (NNSFC)[71631008] ; NNSFC[11331011] ; Ministry of Science and Technology of China[2016YFB0502301] ; NSF by NNSFC[DMS-1620898] ; NSF by NNSFC[11529101] ; National Cancer Institute[U01-CA057030]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000475163100001
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/35052
专题	系统科学研究所
通讯作者	Liang, Hua
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 2.Qingdao Univ, Sch Math & Stat, Qingdao, Shandong, Peoples R China 3.Capital Normal Univ, Sch Math Sci, Beijing, Peoples R China 4.George Washington Univ, Dept Stat, 801 22nd St NW, Washington, DC 20052 USA 5.Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA 6.Univ Technol Sydney, Ultimo, Australia
推荐引用方式 GB/T 7714	Zhang, Xinyu,Zou, Guohua,Liang, Hua,et al. Parsimonious Model Averaging With a Diverging Number of Parameters[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2019:13.
APA	Zhang, Xinyu,Zou, Guohua,Liang, Hua,&Carroll, Raymond J..(2019).Parsimonious Model Averaging With a Diverging Number of Parameters.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,13.
MLA	Zhang, Xinyu,et al."Parsimonious Model Averaging With a Diverging Number of Parameters".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (2019):13.