Recover the spectrum of covariance matrix: a non-asymptotic iterative method

TL;DR

This paper introduces 'Concent', an iterative algorithm designed to correct the bias in sample covariance spectra, effectively recovering the true spectrum in small to moderate dimensions.

Contribution

The paper presents a novel iterative method that actively eliminates bias in covariance spectrum estimation, improving accuracy over traditional approaches.

Findings

'Concent' accurately recovers true spectra in simulated data.

The method outperforms existing bias correction techniques.

Effective for small and moderate-dimensional datasets.

Abstract

It is well known the sample covariance has a consistent bias in the spectrum, for example spectrum of Wishart matrix follows the Marchenko-Pastur law. We in this work introduce an iterative algorithm 'Concent' that actively eliminate this bias and recover the true spectrum for small and moderate dimensions.