Selection of the number of regression variables; A minimax choice of generalized FPE
A generalized Final Prediction Error \((FPE_{\alpha})\) criterion is considered. Based on n observations, the number k of regression variables is selected from a given range \(0\leq k\leq K\), so as to minimize \(FPE_{\alpha}(k)=n{\hat \sigma}^ 2(k)+\alpha k\{n{\hat \sigma}^ 2(k)/(n-K)\}\). It is shown that if \(\alpha\) tends to infinity with n, the selection is consistent but the maximum of the mean squared error of estimates of parameters diverges to infinity with the same order of divergence as that of \(\alpha\). A meaningful minimax choice of \(\alpha\) exists for a regret type mean squared error, while for simple mean squared error it is trivially 0. The minimax regret choice of \(\alpha\) converges to a constant, approximately 3.5 for \(K\geq 8\) if n-K increases simultaneously with n, otherwise it diverges to infinity with n.
selection of the number of regression variables
scientific article; zbMATH DE number 4005372
scientific article