Browsing by Author "Toyoda, T"

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    Estimation of variance after a preliminary test of homogeneity and optimal levels of significance for the pre-test
    (1975) Toyoda, T; Wallace, TD
    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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    Optimal Critical Values for Pre-Testing in Regression
    (1976) Toyoda, T; Wallace, TD
    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.