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Asymptotic optimality of a cross-validatory predictive approach to linear model selection

Arijit Chakrabarti and Tapas Samanta

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Abstract

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.

Chapter information

Source
Bertrand Clarke and Subhashis Ghosal, eds., Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 138-154

Dates
First available in Project Euclid: 28 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1209398466

Digital Object Identifier
doi:10.1214/074921708000000110

Mathematical Reviews number (MathSciNet)
MR2459222

Subjects
Primary: 62J05: Linear regression
Secondary: 62F15: Bayesian inference

Keywords
cross-validation oracle predictive density

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Chakrabarti, Arijit; Samanta, Tapas. Asymptotic optimality of a cross-validatory predictive approach to linear model selection. Pushing the Limits of Contemporary Statistics: Contributions in Honor of Jayanta K. Ghosh, 138--154, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/074921708000000110. https://projecteuclid.org/euclid.imsc/1209398466


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