Location‐invariant Multi‐sample U‐tests for Covariance Matrices with Large Dimension
针对两个或多个多元分布具有共同协方差矩阵的情形，当向量维度可能超过样本数时，提出了基于位置不变U统计量的检验统计量，并推导了其渐近分布，适用于小或中等样本量和大维度场景。
Abstract For two or more multivariate distributions with common covariance matrix, test statistics for certain special structures of the common covariance matrix are presented when the dimension of the multivariate vectors may exceed the number of such vectors. The test statistics are constructed as functions of location‐invariant estimators defined as U ‐statistics, and the corresponding asymptotic theory is used to derive the limiting distributions of the proposed tests. The properties of the test statistics are established under mild and practical assumptions, and the same are numerically demonstrated using simulation results with small or moderate sample sizes and large dimensions.