R-NL: Covariance Matrix Estimation for Elliptical Distributions based on Nonlinear Shrinkage

TL;DR

This paper introduces a robust and efficient covariance matrix estimator for elliptical distributions that combines Tyler's estimator with nonlinear shrinkage, demonstrating superior performance in simulations and real data applications.

Contribution

It proposes a novel covariance estimation method that integrates Tyler's estimator with nonlinear shrinkage, ensuring robustness and computational efficiency in high-dimensional elliptical models.

Findings

Converges reliably in iterative procedures.

Outperforms existing estimators in simulations.

Achieves state-of-the-art results on real data.

Abstract

We combine Tyler's robust estimator of the dispersion matrix with nonlinear shrinkage. This approach delivers a simple and fast estimator of the dispersion matrix in elliptical models that is robust against both heavy tails and high dimensions. We prove convergence of the iterative part of our algorithm and demonstrate the favorable performance of the estimator in a wide range of simulation scenarios. Finally, an empirical application demonstrates its state-of-the-art performance on real data.