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基于单个特征根的两个协方差矩阵相等检验：功效比较AI 解读

Exact non-central distributions of individual characteristic roots have been obtained in two- and three-roots cases in connection with tests of the hypothesis σ1=σ2, where σ1 and σ2 are covariance matrices of two p-variate normal populations. Powers of tests using individual roots are tabulated for the test of this hypothesis against various one-sided simple alternatives and comparisons of powers made.

基于四种准则的两协方差矩阵相等检验的功效比较AI 解读

Exact non-central c.d.f.'s of four criteria in the two-roots case are derived for tests of the hypothesis Σ1 = Σ2 against one-sided alternatives, where Σ1 and Σ2 are covariance matrices of two normal populations. The tests are based on Roy's largest root, and on Lawley-Hotelling's, Pillai's and Wilks's criteria. Powers of the last three criteria have been tabulated extensively, and power comparisons have been made between the three, and also with the largest root, whose…

基于四种准则的协方差矩阵相等检验功效比较AI 解读

Exact non-central c.d.f.'s of four criteria in the two-roots case are derived for tests of the hypothesis Σ1 = Σ2 against one-sided alternatives, where Σ1 and Σ2 are covariance matrices of two normal populations. The tests are based on Roy's largest root, and on Lawley-Hotelling's, Pillai's and Wilks's criteria. Powers of the last three criteria have been tabulated extensively, and power comparisons have been made between the three, and also with the largest root, whose…

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四种准则下两类多元假设检验的功效比较AI 解读

Tests of two hypotheses are considered in this paper, namely, (i) the independence between ap-set and a q-set of variates in a (p + q)-variate normal population, and (ii) the equality of mean vectors of lp-variate normal populations having a common covariance matrix, based on the following four test criteria: (1) Roy's largest root criterion, (2) U(p), a constant times Hotelling's T02: criterion, (3) Pillai's V(p) criterion and (4) Wilks's criterion. For p = 2, the exact…

多元分析中矩阵最大特征根的上尾分位点AI 解读

The general expressions obtained by Pillai (1965) for approximating at the upper end to the C.D.F. of the largest of s characteristic roots of a matrix jointly distributed according to the Fisher-Girshick-Hsu-Roy distribution, have been used to compute upper 5 and 1 % points of the largest root for s up to 20, of which those for s = 14, 16, 18 and 20 are presented in this paper. Methods of interpolation for obtaining such percentage points for intermediate values of s have…

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相关正态变量次序统计量的线性函数及其比值分布：侧重极差AI 解读

This paper deals with the distribution of linear functions and ratios of linear functions of order statistics from an equally correlated set of normal random variables. Some special cases of this family of linear functions are considered. The case of range is studied in great detail both for the case of equal correlations as well as in the general case. For the general case, formulse for the distribution of range are obtained for sample sizes of two, three and four. In the…

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