The Mann-Whitney U-statistic for $\alpha$-dependent sequences

TL;DR

This paper analyzes the asymptotic behavior of the Mann-Whitney U-statistic for independent stationary sequences, including dependent and non-mixing processes, and proposes corrected tests for stochastic domination based on these theoretical insights.

Contribution

It provides the first asymptotic results for the Mann-Whitney U-statistic in the context of short-range dependent and non-mixing sequences, and introduces corrected tests for stochastic domination.

Findings

Asymptotic behavior established for short-range dependent sequences.

Corrected tests perform well in simulations with non-mixing processes.

Partial results obtained for long-range dependence cases.

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.