Econometrica: Mar, 1976, Volume 44, Issue 2

Optimal Critical Values for Pre-Testing in Regression

https://doi.org/0012-9682(197603)44:2<365:OCVFPI>2.0.CO;2-C
p. 365-375

T. D. Wallace, T. Toyoda

In this paper we derive and present optimal critical points for pre-tests in regression using a minimum average relative risk criterion. We use the same type risk functions as Sawa and Hiromatsu [8] who, in a recent paper in this journal, derived pre-test critical values using a minimax regret criterion. Since James-Stein type estimators can be shown to dominate any pre-test estimator for the risk functions used here and in [8], no normative claims are made for the critical values we give. However, the use of pre-testing procedures continues in practice and the results given here, contrasted with other results, add to information about the character of costs and returns to such practices.