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Parsimonious Model Averaging With a Diverging Number of Parameters
Zhang, Xinyu1,2; Zou, Guohua3; Liang, Hua4; Carroll, Raymond J.5,6
2019-06-18
Source PublicationJOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN0162-1459
Pages13
AbstractModel 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.
KeywordAsymptotic optimality Frequentist model averaging Jackknife model averaging Mallows model averaging Parsimony
DOI10.1080/01621459.2019.1604363
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000475163100001
PublisherAMER STATISTICAL ASSOC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35052
Collection系统科学研究所
Corresponding AuthorLiang, Hua
Affiliation1.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
Recommended Citation
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.
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