Estimation of variance after a preliminary test of homogeneity and optimal levels of significance for the pre-test
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The question of whether to pool two samples in variance estimation is often decided via a preliminary F test. In this paper we show that the optimal pre-test F value is unity for a onesided alternative, where the objective function is to minimize average relative risk. The outcome is independent of numbers of degrees of freedom in each sample. Optimal significance levels vary somewhat but are close to + for most d.f. and equal to : when numerator and denominator d.f. are equal. The results also apply to regression variance estimation across two data regimes.
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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