  The problem of model selection is inevitable in an increasingly large number
of applications involving partial theoretical knowledge and vast amounts of
information, like in medicine, biology or economics. The associated techniques
are intended to determine which variables are "important" to "explain a
phenomenon under investigation. The terms "important" and "explain" can have
very different meanings according to the context and, in fact, model selection
can be applied to any situation where one tries to balance variability with
complexity. In this paper, we introduce a new class of error measures and of
model selection criteria, to which many well know selection criteria belong.
Moreover, this class enables us to derive a novel criterion, based on a
divergence measure between the predictions produced by two nested models,
called the Prediction Divergence Criterion (PDC). Our selection procedure is
developed for linear regression models, but has the potential to be extended to
other models. We demonstrate that, under some regularity conditions, it is
asymptotically loss efficient and can also be consistent. In the linear case,
the PDC is a counterpart to Mallow's Cp but with a lower asymptotic probability
of overfitting. In a case study and by means of simulations, the PDC is shown
to be particularly well suited in "sparse" settings with correlated covariates
which we believe to be common in real applications.
