Analysis of a multi-target linear shrinkage covariance estimator

TL;DR

This paper introduces a multi-target linear shrinkage estimator for covariance matrices, combining multiple targets with the sample covariance, and demonstrates its theoretical convergence and empirical superiority over existing methods.

Contribution

It derives the first multi-target linear shrinkage estimator with proven convergence and empirical performance improvements over standard estimators.

Findings

Outperforms standard covariance estimators in various scenarios

Proven convergence towards the oracle estimator under Kolmogorov asymptotics

Provides both exact and empirical mean estimators for practical use

Abstract

Multi-target linear shrinkage is an extension of the standard single-target linear shrinkage for covariance estimation. We combine several constant matrices - the targets - with the sample covariance matrix. We derive the oracle and a \textit{bona fide} multi-target linear shrinkage estimator with exact and empirical mean. In both settings, we proved its convergence towards the oracle under Kolmogorov asymptotics. Finally, we show empirically that it outperforms other standard estimators in various situations.