Adaptive model selection

X. Shen; J. Ye

doi:10.1198/016214502753479356

Adaptive model selection

X. Shen, J. Ye

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

122 Scopus citations

Abstract

Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for "small" models and poorly for "large" models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed procedure, combining the benefit of a class of nonadaptive procedures, approximates the best performance Of this class of procedures across a variety of different situations. This class includes many well-known procedures, such as AIC, BIC, Mallows's C _p, and risk inflation criterion (RIC). The proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression. Simulation results and an asymptotic analysis support the effectiveness of the proposed procedure.

Original language	English (US)
Pages (from-to)	210-221
Number of pages	12
Journal	Journal of the American Statistical Association
Volume	97
Issue number	457
DOIs	https://doi.org/10.1198/016214502753479356
State	Published - Mar 2002

Bibliographical note

Funding Information:
XiaotongShenisAssociatePro,fDepartmentsesofoStatistics,r TheOhio StateUn,Coiluvmbes,OHur4s31i02(t-yEmilxshen: a@stat.ohio-state.eu)d. Jianming Ye isAsPsroo,cfSeainatRsstsDoesoertpofAccouarn-tmen tancy, Baruch Cllege,oCitUy noiNvfweYoerrkNs,1i0Yt00y(1E-mail: jianming_ye@baruch.cuny.eu)Sd.eshnrse’ewaasrspcuopehdrintpabryt National Science Foundation grant DMS-0072635 and OŽ ce foNvl aa Resegarant rN00c014h-99-1-0214. Ye gratefllyuacknowledges the Ž nancial support of the Zicklin School of Business, Baruch College. The authors also thank the associate editor and anonymous resfforeveryrhelpefulecomments and suggestions.

Keywords

Adaptive penalty
False discovery rate
Optimal predication
Parametric and nonparametric regression
Variable selection
Wavelets

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10.1198/016214502753479356

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year = "2002",

month = mar,

doi = "10.1198/016214502753479356",

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N2 - Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for "small" models and poorly for "large" models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed procedure, combining the benefit of a class of nonadaptive procedures, approximates the best performance Of this class of procedures across a variety of different situations. This class includes many well-known procedures, such as AIC, BIC, Mallows's C p, and risk inflation criterion (RIC). The proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression. Simulation results and an asymptotic analysis support the effectiveness of the proposed procedure.

AB - Most model selection procedures use a fixed penalty penalizing an increase in the size of a model. These nonadaptive selection procedures perform well only in one type of situation. For instance, Bayesian information criterion (BIC) with a large penalty performs well for "small" models and poorly for "large" models, and Akaike's information criterion (AIC) does just the opposite. This article proposes an adaptive model selection procedure that uses a data-adaptive complexity penalty based on a concept of generalized degrees of freedom. The proposed procedure, combining the benefit of a class of nonadaptive procedures, approximates the best performance Of this class of procedures across a variety of different situations. This class includes many well-known procedures, such as AIC, BIC, Mallows's C p, and risk inflation criterion (RIC). The proposed procedure is applied to wavelet thresholding in nonparametric regression and variable selection in least squares regression. Simulation results and an asymptotic analysis support the effectiveness of the proposed procedure.

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KW - Variable selection

KW - Wavelets

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ER -

Adaptive model selection

Abstract

Bibliographical note

Keywords

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