On the choice of penalty term in generalized FPE criterion

In variable selection, many existing selection criteria are closely related to the generalized final prediction error (FPE) criterion. In the linear regression context, the FPE criterion amounts to minimizing C(k, λ) = RSS(k)+λkσ2 over k, where k is the number of parameters in the model, RSS(k) is the residual sum of squares and σ2 is some estimate of the error variance. Different values of λ give different selection criteria. This article presents some useful results on the choice of λ. Some insights are obtained. Application to the study of the multifold cross validation criterion is also discussed.