Asymptotic optimality of a cross-validatory predictive approach to linear model selection
Arijit Chakrabarti, Tapas Samanta
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.
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Primary Subjects: 62J05
Secondary Subjects: 62F15
Keywords: cross-validation; oracle; predictive density
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.imsc/1209398466
Digital Object Identifier: doi:10.1214/074921708000000110
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