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多元线性假设检验中 Wilks 统计量非零假设分布的渐近展开AI 解读

An asymptotic expansion of the nonnull distribution of the Wilks statistic for testing the linear hypothesis in multivariate analysis of variance is obtained up to the order $N^{-2}$ where $N$ is the sample size, for the first time in terms of noncentral beta distributions. The asymptotic distributions are better than the ones available in Anderson (1958) in the null case and in Sugiura and Fujikoshi (1969) and Posten and Bergman (1964) in the nonnull case. In fact, for…

一类多元分析统计量的分布AI 解读

In this article, exact and asymptotic distributions of a class of statistics whose moments are of a particular form have been obtained. An application to Wilks's criterion for testing a linear hypothesis is given, and it is shown by numerical comparison that the first term of the asymptotic expansion of the distribution obtained in this article is better than Box's asymptotic expansion in terms of chisquared distributions. The exact distribution is easily computable and has…

检验指定协方差矩阵的似然比统计量分布AI 解读

The exact null distribution of the likelihood ratio criterion for testing the null hypothesis Σ θ σ0 against the alternative Σ ≠ Σ0 in Np(μ, Σ) has been obtained in a series form and percentage points computed for p θ 2 (1) 10 for α θ 0.005, 0.01, 0.025, 0.05, 0.1 and 0.25 and various degrees of freedom, but only selected tables are presented here.

检验指定协方差矩阵的似然比准则分布AI 解读

The exact null distribution of the likelihood ratio criterion for testing the null hypothesis Σ θ σ0 against the alternative Σ ≠ Σ0 in Np(μ, Σ) has been obtained in a series form and percentage points computed for p θ 2 (1) 10 for α θ 0.005, 0.01, 0.025, 0.05, 0.1 and 0.25 and various degrees of freedom, but only selected tables are presented here.