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August 2008 Evaluation and selection of models for out-of-sample prediction when the sample size is small relative to the complexity of the data-generating process
Hannes Leeb
Bernoulli 14(3): 661-690 (August 2008). DOI: 10.3150/08-BEJ127

Abstract

In regression with random design, we study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration are correct. Our analysis is based on explicit finite-sample results. Our main findings differ from those of other analyses that are based on traditional large-sample limit approximations because we consider a situation where the sample size is small relative to the complexity of the data-generating process, in the sense that the number of parameters in a ‘good’ model is of the same order as sample size. Also, we allow for the case where the number of candidate models is (much) larger than sample size.

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Hannes Leeb. "Evaluation and selection of models for out-of-sample prediction when the sample size is small relative to the complexity of the data-generating process." Bernoulli 14 (3) 661 - 690, August 2008. https://doi.org/10.3150/08-BEJ127

Information

Published: August 2008
First available in Project Euclid: 25 August 2008

zbMATH: 1155.62029
MathSciNet: MR2537807
Digital Object Identifier: 10.3150/08-BEJ127

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

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Vol.14 • No. 3 • August 2008
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