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.
"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