Multivariate analysis of variance and change points estimation for high‐dimensional longitudinal data
Multivariate analysis of variance and change points estimation for high‐dimensional longitudinal data
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DOI：
10.1111/sjos.12460
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发表时间：
2020-04
影响因子：
1
通讯作者：
Pingshou Zhong;Jun Li;P. Kokoszka
中科院分区：
文献类型：
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作者：
Pingshou Zhong;Jun Li;P. Kokoszka
本文考虑了n个被试在T次上重复测量的p维总体均值向量的时间齐性检验问题。为了应对高维纵向数据带来的挑战，我们提出了一种既考虑大p、大T、小n的情况，又考虑复杂的时空相关性的方法。我们同时考虑了多元方差分析问题和变点问题。在较温和的条件下，建立了所提出的检验统计量的渐近分布。在变点设置中，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进制分割方法，证明了它与显式依赖于p、T和n的比率是一致的。仿真研究和对fMRI数据的应用验证了所提方法的性能和适用性。
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.