Asymptotic mean efficiency of a selection of regression variables (Q1057602)

To compare different procedures for selection of regression variables, a mean efficiency concept is introduced, which is an extension of the concept of efficiency previously introduced by the author [Biometrika 68, 45-53 (1981; Zbl 0464.62054)]. Without any stronger assumption, we can show that the FPE procedure or the AIC procedure or the \(C_ p\) procedure are all asymptotically mean efficient, under the assumption that the number of regression variables be infinite or increase with the sample size.