Robust Change-Point Detection Based on Sliding-Window Mann-Whitney U Statistics

In statistical signal processing, online change-point detection often faces the challenge of impulsive noise, which severely degrades standard algorithms. While the sliding-window centered Mann-Whitney U statistic (CMWUS) offers a robust and computationally efficient non-parametric alternative, its practical deployment is hindered by uncontrolled false alarm rates (FAR). This limitation arises because conventional implementations rely on static thresholds that ignore the strong temporal correlations introduced by the sliding-window mechanism. To achieve rigorous FAR control over indefinite monitoring horizons, we comprehensively establish the stochastic properties of the CMWUS sequence under the null cases (no change point). Specifically, we prove its strict stationarity, derive a closed-form autocorrelation function (ACF), and establish the ACF's mean-square ergodicity. These theoretical contributions directly enable the construction of the sequence's approximate multivariate joint distribution, facilitating a novel dynamic thresholding strategy. Numerical experiments confirm that the proposed framework outperforms representative parametric (CUSUM) and competitive non-parametric (NUNCL) baselines, particularly in achieving stringent localization precision under heavy-tailed noise environments.