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.

中文翻译：

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α依赖序列的Mann-Whitney U统计

对于两个独立的平稳序列，我们给出了Mann-Whitney U统计量的渐近行为。结果适用于一大类短程相关序列，包括Rosenblatt所指的许多非混合过程[17]。在长期依赖的案例中，我们还给出了部分结果，并且我们调查了其他相关问题。根据理论结果，我们对随机支配的常规检验提出了一些简单的修正。接下来，我们模拟不同的（非混合）平稳过程，看校正后的测试效果良好。