Journal
BERNOULLI
Volume 14, Issue 3, Pages 661-690Publisher
INT STATISTICAL INST
DOI: 10.3150/08-BEJ127
Keywords
generalized cross validation; large number of parameters and small sample size; model selection; nonparametric regression; out-of-sample prediction; S-p criterion
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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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