Asymptotic optimality of a cross-validatory predictive approach to linear model selection
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.
Cite
@article{arxiv.0805.3238,
title = {Asymptotic optimality of a cross-validatory predictive approach to linear model selection},
author = {Arijit Chakrabarti and Tapas Samanta},
journal= {arXiv preprint arXiv:0805.3238},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/074921708000000110 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)