Weighted Statistic in Detecting Faint and Sparse Alternatives for High-Dimensional Covariance Matrices
提出一种数据驱动的加权检验统计量，用于高维协方差矩阵相等性检验，在微弱和稀疏备择假设下均表现优异，模拟验证其优于现有方法。
This article considers testing equality of two population covariance matrices when the data dimension p diverges with the sample size n (p/n → c > 0). We propose a weighted test statistic that is data-driven and powerful in both faint alternatives (many small disturbances) and sparse alternatives (several large disturbances). Its asymptotic null distribution is derived by large random matrix theory without assuming the existence of a limiting cumulative distribution function of the population covariance matrix. The simulation results confirm that our statistic is powerful against all alternatives, while other tests given in the literature fail in at least one situation. Supplementary materials for this article are available online.