Optimal Critical Values for Pre-Testing in Regression
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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  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 , 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.
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James B. Duke Professor Emeritus of Economics
Professor Wallace’s most recent endeavor was the completion of a textbook covering general knowledge within his field. The book was Econometrics: An Introduction, written in collaboration with his former student, Lew Silver. As a researcher, his investigations explored such variables as human capital accumulation, linear restrictions in regression, time series data, multicollinearity and low-order moments in stable lag distribution, fertility and replacement, full time schooling, the mean squa