In this article, we develop a modern perspective on Akaike's Information
Criterion and Mallows' Cp for model selection. Despite the diff erences in
their respective motivation, they are equivalent in the special case of
Gaussian linear regression. In this case they are also equivalent to a third
criterion, an unbiased estimator of the quadratic prediction loss, derived from
loss estimation theory. Our first contribution is to provide an explicit link
between loss estimation and model selection through a new oracle inequality. We
then show that the form of the unbiased estimator of the quadratic prediction
loss under a Gaussian assumption still holds under a more general
distributional assumption, the family of spherically symmetric distributions.
One of the features of our results is that our criterion does not rely on the
speci ficity of the distribution, but only on its spherical symmetry. Also this
family of laws o ffers some dependence property between the observations, a
case not often studied