Many-sample tests for the equality and the proportionality hypotheses between large covariance matrices

Tianxing Mei, Chen Wang, Jianfeng Yao
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Abstract

This paper proposes procedures for testing the equality hypothesis and the proportionality hypothesis involving a large number of $q$ covariance matrices of dimension $p\times p$. Under a limiting scheme where $p$, $q$ and the sample sizes from the $q$ populations grow to infinity in a proper manner, the proposed test statistics are shown to be asymptotically normal. Simulation results show that finite sample properties of the test procedures are satisfactory under both the null and alternatives. As an application, we derive a test procedure for the Kronecker product covariance specification for transposable data. Empirical analysis of datasets from the Mouse Aging Project and the 1000 Genomes Project (phase 3) is also conducted.
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大型协方差矩阵之间的相等假设和比例假设的多样本检验
本文提出了涉及大量维数为 $p/times p$ 的 $q$ 协方差矩阵的相等假设和比例假设检验程序。在一个限制方案下,即 $p$、$q$ 和来自 $q$ 种群的样本量以适当的方式增长到无穷大,所提出的检验统计量被证明是渐近正态的。模拟结果表明,检验程序的有限样本特性在零样本和替代样本下都是令人满意的。作为应用,我们推导出了可传递数据的 Kronecker 乘积协方差规范的检验程序。我们还对小鼠衰老项目和 1000 基因组项目(第 3 阶段)的数据集进行了实证分析。
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