Correspondence Ping-Shou Zhong, Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045. Email: pszhong@uic.edu Abstract This article considers the problem of testing temporal homogeneity of p-dimensional population mean vectors from repeated measurements on n subjects over T times. To cope with the challenges brought about by high-dimensional longitudinal data, we propose methodology that takes into account not only the “large p, large T, and small n” situation but also the complex temporospatial dependence. We consider both the multivariate analysis of variance problem and the change point problem. The asymptotic distributions of the proposed test statistics are established under mild conditions. In the change point setting, when the null hypothesis of temporal homogeneity is rejected, we further propose a binary segmentation method and show that it is consistent with a rate that explicitly depends on p,T, and n. Simulation studies and an application to fMRI data are provided to demonstrate the performance and applicability of the proposed methods.

中文翻译：

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高维纵向数据的方差和变化点估计的多变量分析

Ping-Shou Zhong，数学、统计学和计算机科学，伊利诺伊大学芝加哥分校，851 S. Morgan Street, Chicago, IL 60607-7045。电子邮件：pszhong@uic.edu 摘要 本文考虑了测试 p 维总体均值向量的时间同质性问题，该问题来自对 n 个对象在 T 次重复测量。为了应对高维纵向数据带来的挑战，我们提出的方法不仅要考虑“大p、大T、小n”的情况，还要考虑复杂的时间空间依赖性。我们同时考虑方差问题和变化点问题的多元分析。建议的检验统计量的渐近分布是在温和条件下建立的。在更改点设置中，当时间同质性的零假设被拒绝时，我们进一步提出了一种二元分割方法，并表明它与明确依赖于 p、T 和 n 的速率一致。提供了模拟研究和对 fMRI 数据的应用，以证明所提出方法的性能和适用性。