# Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Model

arXiv: https://arxiv.org/abs/1506.00691 · HTML: https://mlsanity.com/paper/1506.00691/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2015.

## Built on by (most cited first, 30 of 47)

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## Abstract (arXiv)

Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of covariance matrices, but are also robust to outliers from arbitrary sources. In this paper, we define a new concept called matrix depth and then propose a robust covariance matrix estimator by maximizing the empirical depth function. The proposed estimator is shown to achieve minimax optimal rate under Huber's ε-contamination model for estimating covariance/scatter matrices with various structures including bandedness and sparsity.