Browsing by Author "Wallace, TD"

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    Estimating the error variance in regression after a preliminary test of restrictions on the coefficients
    (1987) Clarke, JA; Giles, DEA; Wallace, TD
    Maximum-likelihood estimation of the variance of the disturbances in a linear regression is considered in the context of exact linear restrictions on the coefficient vector. The exact risk function for the associated preliminary-test estimator of this variance is derived and evaluated numerically on the basis of relative quadratic loss. Our results indicate that in practical situations the risk of the pre-test estimator differs only slightly from that of the naive estimator which ignores the restrictions without testing. Applying the coefficient restrictions without testing their validity is not recommended.
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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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    Full-Time Schooling in Life-Cycle Models of Human Capital Accumulation
    (1975) Wallace, TD; Ihnen, LA
    A reduced-form equation relating length of "formal schooling" to market, endowment, and ability parameters was derived for a life-cycle human capital accumulation model with alternative assumptions: (a) equal borrowing and lending rates and (b) no loans for human capital investment. Length of "formal schooling" increases when loans are unavailable. For both cases, length of "formal schooling" varies directly with length of work life, a Hicks-neutral "ability" index, and the ratio of the human capital rental rate to the price of associated inputs, and varies inversely with the discount rate, deterioration rate, and initial human capital stock.
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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.