Asymptotical optimality of Akaike's final prediction error

Abstract

Akaike's FPE procedure as a data dependent method of selecting the degree and the number of pieces of a piece wise polynomial estimator of a regression function is proposed here. The proposed method requires no assumption of smoothness of the regression function. It is shown the asymptotic efficiency of FPE is achieved both in a.s. convergence and in theg-th mean convergence.