# The Minimum Regularized Covariance Determinant estimator

arXiv: https://arxiv.org/abs/1701.07086 · HTML: https://mlsanity.com/paper/1701.07086/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2017.

## Built on by (most cited first, 5 of 5)

- [The Cellwise Minimum Covariance Determinant Estimator](https://mlsanity.com/paper/2207.13493/) (2022)
- [Sparse outlier-robust PCA for multi-source data](https://mlsanity.com/paper/2407.16299/) (2024)
- [Edgewise outliers of network indexed signals](https://mlsanity.com/paper/2307.11239/) (2023)
- [Efficient Computation of Sparse and Robust Maximum Association Estimators](https://mlsanity.com/paper/2311.17563/) (2023)
- [Anomaly Detection in High-Dimensional Bank Account Balances via Robust Methods](https://mlsanity.com/paper/2511.11143/) (2025)

## Abstract (arXiv)

The Minimum Covariance Determinant (MCD) approach robustly estimates the location and scatter matrix using the subset of given size with lowest sample covariance determinant. Its main drawback is that it cannot be applied when the dimension exceeds the subset size. We propose the Minimum Regularized Covariance Determinant (MRCD) approach, which differs from the MCD in that the scatter matrix is a convex combination of a target matrix and the sample covariance matrix of the subset. A data-driven procedure sets the weight of the target matrix, so that the regularization is only used when needed. The MRCD estimator is defined in any dimension, is well-conditioned by construction and preserves the good robustness properties of the MCD. We prove that so-called concentration steps can be performed to reduce the MRCD objective function, and we exploit this fact to construct a fast algorithm. We verify the accuracy and robustness of the MRCD estimator in a simulation study and illustrate its practical use for outlier detection and regression analysis on real-life high-dimensional data sets in chemistry and criminology.