This paper deals with the detection and identification of changepoints among covariances of high-dimensional longitudinal data, where the number of features is greater than both the sample size and the number of repeated measurements. The proposed methods are applicable under general temporal-spatial dependence. A new test statistic is introduced for changepoint detection, and its asymptotic distribution is established. If a changepoint is detected, an estimate of the location is provided. The rate of convergence of the estimator is shown to depend on the data dimension, sample size, and signal-to-noise ratio. Binary segmentation is used to estimate the locations of possibly multiple changepoints, and the corresponding estimator is shown to be consistent under mild conditions. Simulation studies provide the empirical size and power of the proposed test and the accuracy of the changepoint estimator. An application to a time-course microarray dataset identifies gene sets with significant gene interaction changes over time.

中文翻译：

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具有高维纵向数据的协方差矩阵的同质性检验

本文涉及高维纵向数据协方差之间变化点的检测和识别，其中特征的数量大于样本大小和重复测量的数量。所提出的方法适用于一般时空依赖性。为变化点检测引入了新的测试统计量，并建立了其渐近分布。如果检测到变化点，则提供对位置的估计。估计器的收敛速度取决于数据维度、样本大小和信噪比。二进制分割用于估计可能存在多个变化点的位置，并且相应的估计量在温和条件下显示是一致的。模拟研究提供了建议测试的经验大小和功效以及变化点估计器的准确性。对时间进程微阵列数据集的应用识别随时间具有显着基因相互作用变化的基因集。