Harmonic means of Wishart random matrices

被引：2
|
作者：
Lodhia, Asad [1 ]
机构：
[1] Univ Michigan, Dept Stat, 256 West Hall,1085 South Univ Ave, Ann Arbor, MI 48109 USA
来源：
RANDOM MATRICES-THEORY AND APPLICATIONS | 2021年 / 10卷 / 02期
关键词：
Free probability; random matrices; covariance estimation; EIGENVALUE;
D O I：
10.1142/S2010326321500167
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We use free probability to compute the limiting spectral properties of the harmonic mean of n i.i.d. Wishart random matrices W-i whose limiting aspect ratio is gamma is an element of (0, 1) when E[W-i] = I. We demonstrate an interesting phenomenon where the harmonic mean H of the n Wishart matrices is closer in operator norm to E[W-i] than the arithmetic mean A for small n, after which the arithmetic mean is closer. We also prove some results for the general case where the expectation of the Wishart matrices are not the identity matrix.
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页数：24
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