高维样本协方差矩阵极限谱密度的显式表达式

Explicit Expression of Limiting Spectral Density of High Dimensional Sample Covariance Matrices

用Stieltjes变换给出一般高维样本协方差矩阵的极限密度函数的显示表达式,包括:样本元素独立且均值为0,方差为常数的样本协方差矩阵;一个样本协方差矩阵与单位阵的和;样本元素方差不等但只取两值的样本协方差矩阵;两个不同的样本协方差矩阵之和.

Using the method of Stieltjes transform,we gave the explicit expressions of the limiting spectral density functions of the general high dimensional sample covariance matrices,which included：the sample covariance matrix whose elements were independent with zero mean and constant variance;the sum of a sample covariance matrix and a unit matrix;the sample covariance matrix which satisfied that the variance of the elements were different but only had two values;the sum of two different sample covariance matrices.