Jiang Yunlu, Wen Canhong, Jiang Yukang, Wang Xueqin, Zhang Heping
Jinan University, University of Science and Technology of China, Sun Yat-Sen University, Yale University.
Stat Sin. 2023 Oct;33(4):2359-2380. doi: 10.5705/ss.202020.0486.
Testing the equality of two covariance matrices is a fundamental problem in statistics, and especially challenging when the data are high-dimensional. Through a novel use of random integration, we can test the equality of high-dimensional covariance matrices without assuming parametric distributions for the two underlying populations, even if the dimension is much larger than the sample size. The asymptotic properties of our test for arbitrary number of covariates and sample size are studied in depth under a general multivariate model. The finite-sample performance of our test is evaluated through numerical studies. The empirical results demonstrate that our test is highly competitive with existing tests in a wide range of settings. In particular, our proposed test is distinctly powerful under different settings when there exist a few large or many small diagonal disturbances between the two covariance matrices.
检验两个协方差矩阵的相等性是统计学中的一个基本问题，在数据为高维时尤其具有挑战性。通过一种新颖的随机积分方法，我们可以检验高维协方差矩阵的相等性，而无需对两个基础总体假设参数分布，即使维度远大于样本量。在一般的多元模型下，我们深入研究了针对任意数量协变量和样本量的检验的渐近性质。通过数值研究评估了我们检验的有限样本性能。实证结果表明，在广泛的设置下，我们的检验与现有检验相比具有很强的竞争力。特别是，当两个协方差矩阵之间存在一些大的或许多小的对角扰动时，我们提出的检验在不同设置下具有显著的功效。
