This paper considers the problems of detecting a change point and estimating the location in the correlation matrices of a sequence of high-dimensional vectors, where the dimension is large enough to be comparable to the sample size or even much larger. A new break test is proposed based on signflip parallel analysis to detect the existence of change points. Furthermore, a two-step approach combining a signflip permutation dimension reduction step and a CUSUM statistic is proposed to estimate the change point's location and recover the support of changes. The consistency of the estimator is constructed. Simulation examples and real data applications illustrate the superior empirical performance of the proposed methods. Especially, the proposed methods outperform existing ones for non-Gaussian data and the change point in the extreme tail of a sequence and become more accurate as the dimension p increases. Supplementary materials for this article are available online.

翻译：本文考虑了检测变点及估计变点位置的问题，研究对象为一系列高维向量的相关矩阵，其中维度足够大以至于可与样本量媲美甚至远大于样本量。基于符号翻转平行分析，提出了一种新的断裂检验方法以检测变点的存在。此外，结合符号置换降维步骤与CUSUM统计量，提出了一种两步法来估计变点位置并恢复变化的支撑集。给出了估计量的一致性证明。模拟算例与实际数据应用展示了所提方法优越的实证表现。特别地，对于非高斯数据以及序列极端尾部的变点，所提方法优于现有方法，且随着维度p的增加，精度进一步提高。本文的补充材料可在网上获取。