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回归预检验的最优临界值AI 解读

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…

Tables of critical points for the noncentral F are presented with noncentrality equal to 1/2 of numerator degrees of freedom for denominator degrees of freedom of 1-30, 40, 60, 120, 200, 400, and 1,000, and numerator degrees of freedom of 1-30, 40, 60, 120, and 200, and type one errors of 0.05, 0.10, 0.25, and 0.50. These critical points can be used to test the second weak MSE criterion discussed in the companion paper [2]. An approximation is suggested for noncentral F(θ),…

The standard F test for linear restrictions in regression is relevant as a criterion but fails to capture the notion of tradeoff between bias and variance. Average squared distance criteria yield operational tests that are more appropriate, depending upon objectives. In the present paper two alternative criteria are developed. The first allows testing of the hypothesis that the average squared distance of a restricted estimator from the parameter point in k space is less…

回归中精确线性约束的均方误差检验表AI 解读

A table is presented containing critical points for the non-central F with non-centrality of one-half for type one error .05, .10, .25 and .50 and numerator and denominator d.f. including 1–30, 40, 60, 120, 200, 400, 1000. The critical points may be used to test the hypothesis that a set of exact linear restrictions imposed on the parameters of a linear model yield estimators that are better in generalized MSE than the unrestricted, o.l.s., estimators. Tabulation is…

A mixed model of regression with error components is proposed as one of possible interest for combining cross section and time series data. For known variances, it is shown that Aitken estimators and covariance estimators are in one sense asymptotically equivalent, even though the Aitken estimators are more efficient in small samples. Turning to unknown variance components, Zellner-type iterative estimators are compared with covariance estimators. Here, few small sample…

线性回归中参数约束均方误差准则的检验AI 解读

The objectives of this paper are to examine the mean square error criterion for rejecting or adopting restrictions on the parameter space in a regression model, and to develop a uniformly most powerful testing procedure for the criterion. We present a tabulation of critical points for the test for one restriction and selected points of the power function. The mean square error criterion suggests a framework for thinking about the problem of multicollinearity in a linear…

逐步回归估计的效率AI 解读

Much attention has been paid to bias of coefficients resulting from stepwise regressions. Looking at bias alone implies that stepwise estimates are inferior. However, using the criterion of relative mean square errors, it is shown for the two variable case that under certain circumstances, stepwise estimators are “better” than direct least squares estimators.

逐步回归的效率AI 解读

Much attention has been paid to bias of coefficients resulting from stepwise regressions. Looking at bias alone implies that stepwise estimates are inferior. However, using the criterion of relative mean square errors, it is shown for the two variable case that under certain circumstances, stepwise estimators are “better” than direct least squares estimators.