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, Xinyu2,3 ; Zou, Guohua 4; Liang, Hua 5; Carroll, Raymond J.1,6
刊名	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
	2019-06-18
页码	13
关键词	Asymptotic optimality Frequentist model averaging Jackknife model averaging Mallows model averaging Parsimony
ISSN号	0162-1459
DOI	10.1080/01621459.2019.1604363
英文摘要	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.
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
语种	英语
出版者	AMER STATISTICAL ASSOC
WOS记录号	WOS:000475163100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/35051]
专题	系统科学研究所
通讯作者	Liang, Hua
作者单位	1.Univ Technol Sydney, Ultimo, Australia 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Qingdao Univ, Sch Math & Stat, Qingdao, Shandong, Peoples R China 4.Capital Normal Univ, Sch Math Sci, Beijing, Peoples R China 5.George Washington Univ, Dept Stat, 801 22nd St NW, Washington, DC 20052 USA 6.Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA
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.