Detecting changes in high-dimensional vectors presents significant challenges, especially when the post-change distribution is unknown and time-varying. This paper introduces a novel robust algorithm for correlation change detection in high-dimensional data. The approach utilizes the summary statistic of the maximum magnitude correlation coefficient to detect the change. This summary statistic captures the level of correlation present in the data but also has an asymptotic density. The robust test is designed using the asymptotic density. The proposed approach is robust because it can help detect a change in correlation level from some known level to unknown, time-varying levels. The proposed test is also computationally efficient and valid for a broad class of data distributions. The effectiveness of the proposed algorithm is demonstrated on simulated data.

翻译：高维向量中的变化检测面临重大挑战，尤其是在变化后分布未知且时变的情况下。本文提出了一种用于高维数据相关性变化检测的新型鲁棒算法。该方法利用最大幅度相关系数的汇总统计量来检测变化。该汇总统计量不仅捕捉了数据中存在的相关性水平，还具有渐近密度。鲁棒检验正是基于此渐近密度设计而成。所提方法具有鲁棒性，因为它能够帮助检测相关性水平从某个已知水平到未知、时变水平的变化。所提出的检验还具有计算高效性，并适用于广泛的数据分布类别。在模拟数据上验证了所提算法的有效性。