Mathematical Methods of Statistics

, Volume 26, Issue 2, pp 111–133 | Cite as

The Mann–Whitney U-statistic for α-dependent sequences



We give the asymptotic behavior of the Mann–Whitney U-statistic for two independent stationary sequences. The result applies to a large class of short-range dependent sequences, including many nonmixing processes in the sense of Rosenblatt [17]. We also give some partial results in the long-range dependent case, and we investigate other related questions. Based on the theoretical results, we propose some simple corrections of the usual tests for stochastic domination; next we simulate different (nonmixing) stationary processes to see that the corrected tests perform well.


U-statistic weak dependence stationary sequences 

2000 Mathematics Subject Classification

62G30 60F05 


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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Univ. Paris DescartesParisFrance
  2. 2.Univ. Paris Sud, Inst. de Recherche bioMéd. et d’Epidém. du Sport (IRMES) Inst. Natl. du Sport de l’Expertise et de la Performance (INSEP)ParisFrance

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