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

arXiv: https://arxiv.org/abs/2210.14854 · HTML: https://mlsanity.com/paper/2210.14854/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Oct 2022.

## Built on by (most cited first, 1 of 1)

- [Adaptive posterior distributions for uncertainty analysis of covariance matrices in Bayesian inversion problems for multioutput signals](https://mlsanity.com/paper/2501.01148/) (2025)

## Abstract (arXiv)

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.