On the Spectral Density of Large Sample Covariance Matrices with Markov Dependent Columns

TL;DR

This paper studies the spectral distribution of large covariance matrices with columns derived from Markov chains, providing a characterization of their limiting spectral densities through moments.

Contribution

It introduces a novel analysis of spectral densities for covariance matrices with Markov-dependent columns using a moment method approach.

Findings

Characterized limiting spectral densities via moments.

Established convergence of spectral distributions.

Extended spectral analysis to Markov-dependent data.

Abstract

We investigate the spectral distribution of large sample covariance matrices with independent columns and entries in the columns that stem from Markov chains. We characterize the limiting spectral densities by their moments. Correspondingly, the proof is based on a moment method.