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.

T. W. Anderson, Takamitsu Sawa, Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and Their Asymptotic Expansions, Econometrica, Vol. 44, No. 6 (Nov., 1976), p. 1329

Journal Article The Aggregative Structure of Keynes's General Theory Get access Richard T. Froyen Richard T. Froyen University of North Carolina Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 90, Issue 3, August 1976, Pages 369–387, https://doi.org/10.2307/1886039 Published: 01 August 1976