基于F-矩阵的高维协方差矩阵相等性检验

Equality Test of High Dimensional Covariance Matrix Based on F-matrix

在数据维数和样本量都趋于无穷的高维双样本协方差矩阵相等性检验问题中,为了使检验方法更有效,本文结合Xu和Jiang的检验方法,基于随机矩阵理论提出了一个新的检验统计量——TNew,同时利用F-矩阵线性谱统计量的中心极限定理证明了新检验统计量的渐进分布。新的检验方法消除了比例参数的限制,同时对于高维数据下正态和非正态分布都有很好的效果。实验模拟结果表明,新的检验统计量更加稳健。

Based on the equality test of high-dimensional two sample covariance matrix having the data dimensions and sample sizes approaching infinity,we combined Xu testing method with Jiang testing method to make the test more effective,then proposed a new test statistic-TNew through applying random matrix theory.Furthermore,we proved the asymptotic distribution of the new test statistic by using the central limit theorem of linear spectrum statistics of F-matrix.The new test method eliminated the limitation of the scale parameter,and improved both normal and abnormal state.The results showed that,the new test statistic was more robust.