Spectral Moments of Correlated Wishart Matrices

TL;DR

This paper introduces an analytical approach to determine spectral properties of covariance matrices derived from correlated Wishart random matrices, enabling extraction of true correlations from experimental data.

Contribution

It provides exact relations between spectral moments and eigenvalue densities for large matrices, advancing analysis of correlated Wishart matrices.

Findings

Derived explicit formulas for spectral moments

Established connections between eigenvalue densities and spectral moments

Applicable to real-world data analysis for correlation extraction

Abstract

We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral moments and the eigenvalue densities of the covariance matrices and their estimators. The results can be used in practice to extract information about the genuine correlations from the given experimental realization of random matrices.