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Generalized two‐sample U ‐statistics for clustered data
Author(s) -
Lee MeiLing Ting,
Dehling Herold G.
Publication year - 2005
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2005.00298.x
Subject(s) - mathematics , statistics , wilcoxon signed rank test , sample (material) , population , statistic , order statistic , asymptotic distribution , kernel (algebra) , rank (graph theory) , combinatorics , mann–whitney u test , demography , estimator , chemistry , chromatography , sociology
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 byWe derive the asymptotic distribution of U m , n for large sample sizes. As an application we study the generalized Mann–Whitney–Wilcoxon rank sum test for clustered data.