Further results on optimal critical values of pre‐test when estimating the regression error variance

Abstract

Summary This paper enlarges on results of Wan and Zou [Journal of Econometrics 114 (2003), 165–96] on the choice of critical values for pre‐test procedures based on the minimum risk criterion. We consider a modification of the general theorem given in Wan and Zou (2003) to obtain the optimal critical value that minimizes the risks of various inequality pre‐test estimators of the regression error variance under a general class of first‐order differentiable loss functions. Theoretical proofs of earlier numerical results are provided. This paper also presents results on the optimal pre‐test critical values for the simultaneous estimation of the error variance and coefficient vector.