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成对排序与联合排序：再看 Kruskal–Wallis 统计量AI 解读

A test statistic for the k-sample location problem is constructed by appropriately combining all pairwise two-sample Wilcoxon tests. The result is an analogue of the Kruskal-Wallis statistic in the sense that the Pitman asymptotic relative efficiency between the two is one. However, the approximate Bahadur efficiency of the analogue relative to the Kruskal-Wallis statistic is shown to be greater than or equal to one at every alternative.

广义 Behrens–Fisher 问题的 Mood 中位数检验修正AI 解读

A modification of Mood's median test is described which allows one to test for differences between two medians without making any assumptions on the shapes of the underlying populations. The proposed procedure is exactly distribution-free when the populations have the same shape and is asymptotically distribution-free when they do not. It is the retention of the exact distribution-free property when the populations have the same shape which distinguishes the proposed…

联合分布极限定理及其在线性符号秩统计量中的应用札记AI 解读

Summary When investigating the limiting joint distribution of a pair of random variables, it is possible to proceed by studying the associated marginal and conditional distributions. A useful extension of some previous work in this area of Sethuraman is presented by considering the important case when one is conditioning on a lattice-type random variable. The results are applied to obtain, in a simple manner, the limiting distribution of a linear-signed rank statistic.

对称性对非对称性的渐近分布无关检验AI 解读

An asymptotically distribution-free procedure is proposed for testing whether a univariate population is symmetric about some unknown value versus a broad class of asymmetric distribution alternatives. The consistency class of the test is discussed and two competing tests are described, one based on the sample skewness, and the other on Gupta's nonparametric procedure. A Monte Carlo study shows that the proposed test is superior to either competitor since it maintains the…

一类两样本尺度参数的分布自由检验AI 解读

A class of distribution-free statistics for testing equality of two scale parameters when the location parameters are equal is defined. When the two populations are identical, each statistic in this class is governed by the same distribution as that of the two-sample Wilcoxon statistic. A method for selecting which member of the class to use for a particular data set is described, the resulting adaptive procedure being relatively insensitive to small failures in the…

一类两样本尺度参数的分布无关检验AI 解读

A class of distribution-free statistics for testing equality of two scale parameters when the location parameters are equal is defined. When the two populations are identical, each statistic in this class is governed by the same distribution as that of the two-sample Wilcoxon statistic. A method for selecting which member of the class to use for a particular data set is described, the resulting adaptive procedure being relatively insensitive to small failures in the…

摘要暂缺

未来样本中位数的非参数预测区间AI 解读

In this article distribution-free prediction intervals for a future sample median are discussed. Large-sample normal approximations to the coverage probabilities are presented. Asymptotic relative efficiency comparisons are made between the distribution-free procedures and analogous parametric prediction intervals, the resulting values demonstrating the good properties of the nonparametric prediction intervals.

条件渐近正态性的应用AI 解读

Summary Methods for obtaining the limiting distribution of a complicated statistic which depends on another auxiliary statistic are discussed. Examples are given in which a general conditional approach due to Sethuraman is found to be extremely fruitful in solving this type of problem.

分布无关的两样本尺度检验AI 解读

Several linear rank statistics have been proposed in the literature for the two-sample scale problem. We propose a new class of statistics which are distribution free when the populations are identical, but are not linear rank statistics. Our analogs of the Ansari-Bradley, Mood, and Klotz tests are of particular interest. Each has the same Pitman efficiency as its corresponding linear rank statistic, and yet our small-sample power is significantly higher. In addition, our…