Open Access
VOL. 3 | 2008 Asymptotic optimality of a cross-validatory predictive approach to linear model selection
Arijit Chakrabarti, Tapas Samanta

Editor(s) Bertrand Clarke, Subhashis Ghosal

Inst. Math. Stat. (IMS) Collect., 2008: 138-154 (2008) DOI: 10.1214/074921708000000110


In this article we study the asymptotic predictive optimality of a model selection criterion based on the cross-validatory predictive density, already available in the literature. For a dependent variable and associated explanatory variables, we consider a class of linear models as approximations to the true regression function. One selects a model among these using the criterion under study and predicts a future replicate of the dependent variable by an optimal predictor under the chosen model. We show that for squared error prediction loss, this scheme of prediction performs asymptotically as well as an oracle, where the oracle here refers to a model selection rule which minimizes this loss if the true regression were known.


Published: 1 January 2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2459222

Digital Object Identifier: 10.1214/074921708000000110

Primary: 62J05
Secondary: 62F15

Keywords: cross-validation , oracle , predictive density

Rights: Copyright © 2008, Institute of Mathematical Statistics

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