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

2016/11/21 by Dedecker, Jérôme, Saulière, Guillaume
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1611.06828

Abstract

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 non-mixing processes in the sense of Rosenblatt. 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 (non-mixing) stationary processes to see that the corrected tests perform well.

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