A local moment estimator of the spectrum of a large dimensional covariance matrix

TL;DR

This paper introduces a local moment estimator for the spectrum of large-dimensional covariance matrices, capable of handling complex eigenvalue clustering, with proven consistency and demonstrated efficiency through numerical experiments.

Contribution

It generalizes a contour-integral based method to estimate the spectral distribution, applicable even when eigenvalue clusters are not separated.

Findings

Estimator is consistent.

Method works well with non-separated eigenvalue clusters.

Numerical results confirm efficiency.

Abstract

This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment estimation procedure. Compared with the original one, the new procedure can be applied successfully to models where the asymptotic clusters of sample eigenvalues generated by different population eigenvalues are not all separate. The proposed estimates are proved to be consistent. Numerical results illustrate the implementation of the estimation procedure and demonstrate its efficiency in various cases.