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Generalized two‐sample U‐statistics for clustered data

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  • Mei‐Ling Ting Lee
  • Herold G. Dehling

Abstract

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 We derive the asymptotic distribution of Um,n for large sample sizes. As an application we study the generalized Mann–Whitney–Wilcoxon rank sum test for clustered data.

Suggested Citation

  • Mei‐Ling Ting Lee & Herold G. Dehling, 2005. "Generalized two‐sample U‐statistics for clustered data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 59(3), pages 313-323, August.
    • Handle: RePEc:bla:stanee:v:59:y:2005:i:3:p:313-323
    DOI: 10.1111/j.1467-9574.2005.00298.x
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    Cited by:

    1. Denis Larocque & Riina Haataja & Jaakko Nevalainen & Hannu Oja, 2010. "Two sample tests for the nonparametric Behrens–Fisher problem with clustered data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(6), pages 755-771.
    2. Eunhee Kim & Zheng Zhang & Youdan Wang & Donglin Zeng, 2014. "Power calculation for comparing diagnostic accuracies in a multi-reader, multi-test design," Biometrics, The International Biometric Society, vol. 70(4), pages 1033-1041, December.
    3. Haataja, Riina & Larocque, Denis & Nevalainen, Jaakko & Oja, Hannu, 2009. "A weighted multivariate signed-rank test for cluster-correlated data," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1107-1119, July.
    4. Bernard Rosner & Robert J. Glynn & Mei-Ling T. Lee, 2006. "Extension of the Rank Sum Test for Clustered Data: Two-Group Comparisons with Group Membership Defined at the Subunit Level," Biometrics, The International Biometric Society, vol. 62(4), pages 1251-1259, December.

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