In high-dimensional time series, the component processes are often assembled into a matrix to display their interrelationship. We focus on detecting mean shifts with unknown change point locations in these matrix time series. Series that are activated by a change may cluster along certain rows (columns), which forms mode-specific change point alignment. Leveraging mode-specific change point alignments may substantially enhance the power for change point detection. Yet, there may be no mode-specific alignments in the change point structure. We propose a powerful test to detect mode-specific change points, yet robust to non-mode-specific changes. We show the validity of using the multiplier bootstrap to compute the p-value of the proposed methods, and derive non-asymptotic bounds on the size and power of the tests. We also propose a parallel bootstrap, a computationally efficient approach for computing the p-value of the proposed adaptive test. In particular, we show the consistency of the proposed test, under mild regularity conditions. To obtain the theoretical results, we derive new, sharp bounds on Gaussian approximation and multiplier bootstrap approximation, which are of independent interest for high dimensional problems with diverging sparsity.

翻译：在高维时间序列中，分量过程常被组合成矩阵以展示其相互关系。我们专注于检测这些矩阵时间序列中具有未知变点位置的均值偏移。被变化激活的序列可能沿特定行（列）聚类，从而形成模式特定的变点对齐。利用模式特定的变点对齐可显著提升变点检测的功效。然而，变点结构中可能不存在模式特定的对齐。我们提出了一种强大的检验方法，既能检测模式特定的变点，又对非模式特定的变化具有稳健性。我们证明了使用乘数自助法计算所提方法p值的有效性，并推导了检验尺寸与功效的非渐近界。我们还提出了并行自助法，这是一种用于计算所提自适应检验p值的计算高效方法。特别地，我们在温和的正则条件下证明了所提检验的一致性。为获得理论结果，我们推导了高斯近似与乘数自助法近似的新锐界，这些结果对于具有发散稀疏性的高维问题具有独立的研究价值。