# A Concentration of Measure and Random Matrix Approach to Large Dimensional Robust Statistics

arXiv: https://arxiv.org/abs/2006.09728 · HTML: https://mlsanity.com/paper/2006.09728/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jun 2020.

## Built on by (most cited first, 3 of 3)

- [Random Matrix Analysis to Balance between Supervised and Unsupervised Learning under the Low Density Separation Assumption](https://mlsanity.com/paper/2310.13434/) (2023)
- [Concentration of measure for non-linear random matrices with applications to neural networks and non-commutative polynomials](https://mlsanity.com/paper/2507.07625/) (2025)
- [Generalization in Representation Models via Random Matrix Theory: Application to Recurrent Networks](https://mlsanity.com/paper/2511.02401/) (2025)

## Abstract (arXiv)

This article studies the robust covariance matrix estimation of a data collection X = (x1,ldots,xn) with xi = √ τi zi + m, where zi ∈ mathbb Rp is a textitconcentrated vector (e.g., an elliptical random vector), m∈ mathbb Rp a deterministic signal and τi∈ mathbb R a scalar perturbation of possibly large amplitude, under the assumption where both n and p are large. This estimator is defined as the fixed point of a function which we show is contracting for a so-called textitstable semi-metric. We exploit this semi-metric along with concentration of measure arguments to prove the existence and uniqueness of the robust estimator as well as evaluate its limiting spectral distribution.