High-dimensional testing for proportional covariance matrices
High-dimensional testing for proportional covariance matrices
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DOI：
10.1016/j.jmva.2019.01.011
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Koji Tsukuda;S. Matsuura
中科院分区：
文献类型：
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作者：
Koji Tsukuda;S. Matsuura
协方差矩阵比例的假设检验是一个经典的统计问题，在文献中得到了广泛的研究。然而，尽管高维统计推断最近受到了相当大的关注，但在高维环境下对这种测试的处理很少，特别是在变量数量大于样本量的情况下。本文研究了高维环境下两个协方差矩阵m，n≍pδ的比例假设检验问题，其中m，n表示样本量，p表示变量个数，δ∈(1/2，1)。提出了一种检验统计量，并在多元正态分布下得到了它的渐近分布。对所提出的测试方法的非渐近性能进行了数值检验。
Hypothesis testing for the proportionality of covariance matrices is a classical statistical problem and has been widely studied in the literature. However, there have been few treatments of this test in high-dimensional settings, especially for the case where the number of variables is larger than the sample size, despite high-dimensional statistical inference having recently received considerable attention. This paper studies hypothesis testing for the proportionality of two covariance matrices in the high-dimensional setting: m, n≍ p δ for some δ∈(1∕ 2, 1), where m and n denote the sample sizes and p denotes the number of variables. A test statistic is proposed and its asymptotic distribution is derived under multivariate normality. The non-asymptotic performance of the proposed test procedure is numerically examined.