标题： 一个关于两个大尺度协方差矩阵相等的不变性检验 显示英文标题

标题： An Invariant Test for Equality of Two Large Scale Covariance Matrices

摘要： 在本工作中，我们受到张等人（2019）最近工作的启发，研究了一种新的不变检验方法，用于检验两个大规模协方差矩阵的相等性。张等人（2019）提出的两种修正似然比检验（LRTs）是基于Beta矩阵的特征值（或1-特征值）的对数之和。然而，随着维度的增加，Beta矩阵的许多特征值接近0或1，这些修正的LRTs受它们的影响很大。在本工作中，我们则考虑了Beta矩阵的特征值的简单和，并在所有$n_1, n_2, p$以相同速率增加时计算其渐近正态性。我们通过数值实验表明，在我们和他们考虑的所有情况下，我们的检验比张等人（2019）提出的两种修正似然比检验具有更高的功效。 显示英文摘要

摘要： In this work, we are motivated by the recent work of Zhang et al. (2019) and study a new invariant test for equality of two large scale covariance matrices. Two modified likelihood ratio tests (LRTs) by Zhang et al. (2019) are based on the sum of log of eigenvalues (or 1- eigenvalues) of the Beta-matrix. However, as the dimension increases, many eigenvalues of the Beta-matrix are close to 0 or 1 and the modified LRTs are greatly influenced by them. In this work, instead, we consider the simple sum of the eigenvalues (of the Beta-matrix) and compute its asymptotic normality when all $n_1, n_2, p$ increase at the same rate. We numerically show that our test has higher power than two modified likelihood ratio tests by Zhang et al. (2019) in all cases both we and they consider.