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

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.

References in corpus (6)

• Regularized estimation of large covariance matrices
• Covariance regularization by thresholding
• Nonlinear shrinkage estimation of large-dimensional covariance matrices
• Regularized $M$-estimators of scatter matrix
• Regularized Tyler's Scatter Estimator: Existence, Uniqueness, and Algorithms
• Frank-Wolfe-based Algorithms for Approximating Tyler's M-estimator

Cited by in corpus (1)

• Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals