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Generalized two-sample U-statistics for clustered data

机译：聚类数据的广义两样本U统计量

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In a medical context, the two-sample experimental design arises in the context of comparison of two treatments. We have a total of n + m patients of which m receives medication A and n receives medication B. The X_i, 1 < = i < = m, are the observations taken on patients in the first group and the m are the observations taken on patients in the first group, and the Y_k, 1 < = k < = n, are the observations taken on the patients in the second group. One of the most popular tests in nonparametric statistics is Wilcoxon's two-sample rank test. The observations in the first sample, X_i, are independent identically distributed with distribution function F(x) = P(X_i < = x). Similarly, the second sample, Y_j whose distribution function is G(y) = P(Y_i < y). Here, the problem of testing the hypothesis that F = G against the alternative that G is stochastically larger than F, i.e.,that G(x) < = F(x) for all x and that G(x) < F(x) for at least one x. The Mann-Whitney, Wilcoxon test statistic is then given by rejecting the hypothesis for large values of W.
机译：在医学方面，两个样品的实验设计是在两种治疗方法的比较中产生的。我们总共有n + m位患者，其中m位接受药物A和n位接受药物B。X_i，1 <= i <= m，是对第一组患者的观察值，m是对第一组患者的观察值第一组中的患者，Y_k，1 <= k <= n，是对第二组中的患者的观察。非参数统计中最受欢迎的检验之一是Wilcoxon的两样本秩检验。第一个样本X_i中的观测值是独立均匀分布的，分布函数为F（x）= P（X_i <= x）。同样，第二个样本Y_j的分布函数为G（y）= P（Y_i

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