Nonparametric estimate of spectral density functions of sample covariance matrices: A first step

TL;DR

This paper introduces kernel estimators for the spectral density functions of sample covariance matrices, demonstrating their consistency and evaluating their performance through simulations.

Contribution

It proposes a novel nonparametric kernel estimation method for spectral densities of sample covariance matrices, with theoretical consistency proof.

Findings

Kernel estimators are consistent for spectral density functions.

Simulation results show good performance of the estimators.

Method provides a new tool for spectral analysis of covariance matrices.

Abstract

The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the performance of the estimators.