Central limit theorem of nonparametric estimate of spectral density functions of sample covariance matrices

TL;DR

This paper proves a central limit theorem for a kernel-based estimator of the spectral distribution of sample covariance matrices, advancing understanding of their asymptotic behavior.

Contribution

It establishes the CLT for a nonparametric spectral density estimator of sample covariance matrices, extending previous consistency results.

Findings

Proves the CLT for the kernel estimator of spectral distribution.

Provides theoretical foundation for statistical inference on spectral densities.

Enhances understanding of asymptotic properties of covariance matrix estimators.

Abstract

A consistent kernel estimator of the limiting spectral distribution of general sample covariance matrices was introduced in Jing, Pan, Shao and Zhou (2010). The central limit theorem of the kernel estimator is proved in this paper.