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摘要暂缺

摘要暂缺

方差分析中主效应与交互效应的秩检验AI 解读

A class of rank tests for analysis of variance based on linear functions of the Wilcoxon/Mann-Whitney statistics between cells is studied. This class includes many popular procedures. Assuming a location-family model, a condition for optimal Pitman efficacy of tests of main effects in this class is given. Tests for main effects in two-way layouts that achieve this optimality are shown to improve on previous proposals when the sample sizes are unbalanced. Nested orthogonal…

方差分析中主效应与交互效应的秩检验AI 解读

A class of rank tests for analysis of variance based on linear functions of the Wilcoxon/Mann-Whitney statistics between cells is studied. This class includes many popular procedures. Assuming a location-family model, a condition for optimal Pitman efficacy of tests of main effects in this class is given. Tests for main effects in two-way layouts that achieve this optimality are shown to improve on previous proposals when the sample sizes are unbalanced. Nested orthogonal…

敏感且稳健的 p 值AI 解读

We introduce new criteria for evaluating test statistics based on the $p$-values of the statistics. Given a set of test statistics, a good statistic is one which is robust in being reasonably sensitive to all departures from the null implied by that set. We present a constructive approach to finding the optimal statistic. We apply the criteria to two-sided problems; combining independent tests; testing that the mean of a spherical normal distribution is 0, and extensions to…

秩统计量非零假设模型在双变量、两样本与方差分析中的应用AI 解读

A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair…

二元、两样本及方差分析问题中秩统计量的非零假设模型AI 解读

A nonnull model for rank statistics based on Kendall's tau has received quite a bit of attention in the ranking literature lately. In this article, we analyze this model with an eye towards applying it to situations in which nonparametric statistics such as Kendall's tau, the Mann-Whitney/Wilcoxon U, the Jonckheere-Terpstra statistic, the Kruskal-Wallis statistic, and Friedman's statistic for randomized blocks designs are often used. The data for the basic model are a pair…

摘要暂缺

Consider the one-way fixed and balanced analysis of variance model under the assumptions of independence and normality. The problem is to test for homogeneity of variances. A necessary and sufficient condition for admissibility of a test among the class of scale invariant tests is given. Hartley's test and Cochran's test are not in the class and therefore are inadmissible. Various scale invariant tests are examined for parameter consistency. Parameter consistency in this…

一般多元方差分析问题中不变检验的可容许性AI 解读

Necessary and sufficient conditions for an invariant test to be admissible among invariant tests in the general multivariate analysis of variance problem are presented. It is shown that in many cases the popular tests based on the likelihood ratio matrix are inadmissible. Other tests are shown admissible. Numerical work suggests that the inadmissibility of the likelihood ratio test is not serious. The results are given for the multivariate analysis of variance problem as a…

条件独立的 2×2×2 列联表中边际概率的假设检验AI 解读

Consider a 2 × 2 × 2 contingency model with factors A, B, and C. Assume factors A and B are conditionally independent given factor C. We are interested in testing the null hypothesis that the marginal probabilities of the second level of B are the same across the levels of A. Small-sample and large-sample tests are studied.

摘要暂缺

多元单侧备择假设检验的极小完备类AI 解读

In this paper we present minimal complete class theorems for testing problems with simple null hypotheses and multivariate one-sided alternative hypotheses. The results extend previous ones by not requiring that the tests be based on exponentially distributed random variables or that the null and alternative parameter spaces be topologically separated.

独立非中心卡方或F检验的合并AI 解读

The problem of combining several independent Chi squared or $F$ tests is considered. The data consist of $n$ independent Chi squared or $F$ variables on which tests of the null hypothesis that all noncentrality parameters are zero are based. In each case, necessary conditions and sufficient conditions for a test to be admissible are given in terms of the monotonicity and convexity of the acceptance region. The admissibility or inadmissibility of several tests based upon the…

协方差矩阵的不变检验AI 解读

Minimal complete classes of invariant tests are presented for modifications of the problem of testing the independence of $Y$ and $X$, where $(Y, X) \equiv (Y, X_1, \cdots, X_p)$ is a multivariate normal random vector. One modification involves having extra independent observations on $Y$. Others involve extra variates $Z \equiv (Z_1, \cdots, Z_q)$ such that $(Y,X,Z)$ is multivariate normal. Among other results, locally most powerful invariant tests and asymptotically most…