Appropriate penalties in the final prediction error criterion: a decision theoretic approach

The final prediction error (FPE) criterion has been used widely in model selection. The criterion for a linear regression model with k parameters can be written as RSS(k) + [lambda]k2, where RSS(k) is the residual sums of squares, 2 is an unbiased estimate of the error variance and [lambda] is a penalty for complexity. This article considers the simplest situation where the choice is between two Gaussian linear regression models with 2 assumed to be known. We define a signal to noise ratio b for a regression model and use b to restrict the parameter space. The loss function is chosen to be the squared prediction error. Values of [lambda] that are minimax and values of [lambda] that are admissible are found as a function of b.