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Generalized two‐sample U‐statistics for clustered data

In this paper we investigate two‐sample U‐statistics in the case of clusters of repeated measurements observed on individuals from independent populations. The observations on the i‐th individual in the first population are denoted by , 1 ≤ i ≤ m, and those on the k‐th individual in the second population are denoted by , 1 ≤ k ≤ n. Given the kernel φ(x, y), we define the generalized two‐sample U‐statistic by