Asymptotic optimality and efficient computation of the leave-subject-out cross-validation

Handle URI:
http://hdl.handle.net/10754/597623
Title:
Asymptotic optimality and efficient computation of the leave-subject-out cross-validation
Authors:
Xu, Ganggang; Huang, Jianhua Z.
Abstract:
Although the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense that it is asymptotically equivalent to the empirical squared error loss function minimization. An efficient Newton-type algorithm is developed to compute the penalty parameters that optimize the CV criterion. Simulated and real data are used to demonstrate the effectiveness of the leave-subject-out CV in selecting both the penalty parameters and the working correlation matrix. © 2012 Institute of Mathematical Statistics.
Citation:
Xu G, Huang JZ (2012) Asymptotic optimality and efficient computation of the leave-subject-out cross-validation. The Annals of Statistics 40: 3003–3030. Available: http://dx.doi.org/10.1214/12-AOS1063.
Publisher:
Institute of Mathematical Statistics
Journal:
The Annals of Statistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Dec-2012
DOI:
10.1214/12-AOS1063
Type:
Article
ISSN:
0090-5364
Sponsors:
Supported in part by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).Supported in part by NSF Grants DMS-09-07170, DMS-10-07618, DMS-12-08952 and NCI Grant CA57030.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorXu, Ganggangen
dc.contributor.authorHuang, Jianhua Z.en
dc.date.accessioned2016-02-25T12:43:14Zen
dc.date.available2016-02-25T12:43:14Zen
dc.date.issued2012-12en
dc.identifier.citationXu G, Huang JZ (2012) Asymptotic optimality and efficient computation of the leave-subject-out cross-validation. The Annals of Statistics 40: 3003–3030. Available: http://dx.doi.org/10.1214/12-AOS1063.en
dc.identifier.issn0090-5364en
dc.identifier.doi10.1214/12-AOS1063en
dc.identifier.urihttp://hdl.handle.net/10754/597623en
dc.description.abstractAlthough the leave-subject-out cross-validation (CV) has been widely used in practice for tuning parameter selection for various nonparametric and semiparametric models of longitudinal data, its theoretical property is unknown and solving the associated optimization problem is computationally expensive, especially when there are multiple tuning parameters. In this paper, by focusing on the penalized spline method, we show that the leave-subject-out CV is optimal in the sense that it is asymptotically equivalent to the empirical squared error loss function minimization. An efficient Newton-type algorithm is developed to compute the penalty parameters that optimize the CV criterion. Simulated and real data are used to demonstrate the effectiveness of the leave-subject-out CV in selecting both the penalty parameters and the working correlation matrix. © 2012 Institute of Mathematical Statistics.en
dc.description.sponsorshipSupported in part by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).Supported in part by NSF Grants DMS-09-07170, DMS-10-07618, DMS-12-08952 and NCI Grant CA57030.en
dc.publisherInstitute of Mathematical Statisticsen
dc.subjectCross-validationen
dc.subjectGeneralized estimating equationsen
dc.subjectMultiple smoothing parametersen
dc.subjectPenalized splinesen
dc.subjectWorking correlation matricesen
dc.titleAsymptotic optimality and efficient computation of the leave-subject-out cross-validationen
dc.typeArticleen
dc.identifier.journalThe Annals of Statisticsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-CI-016-04en
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