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

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

2008-05-21

arxiv.org/abs/0805.3238v1

IMS Collections 2008, Vol. 3, 138-154

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/074921708000000110 the IMS Collections (http://www.imstat.org/publications/imscollec

Scientific paper

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.

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