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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
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.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ127 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Review of N. Blanford, 'Killing Mr. Lebanon: The Assassination of Rafik Hariri and Its Impact on the Middle East'
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