# Multivariate outlier detection based on a robust Mahalanobis distance with shrinkage estimators

arXiv: https://arxiv.org/abs/1904.02596 · HTML: https://mlsanity.com/paper/1904.02596/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 4 of 4)

- [Optimal Counterfactual Explanations for Scorecard modelling](https://mlsanity.com/paper/2104.08619/) (2021)
- [Accurate and fast anomaly detection in industrial processes and IoT environments](https://mlsanity.com/paper/2404.17925/) (2024)
- [Recovering Imbalanced Clusters via Gradient-Based Projection Pursuit](https://mlsanity.com/paper/2502.02668/) (2025)
- [Efficient Estimation of Regularized Tyler's M-Estimator Using Approximate LOOCV](https://mlsanity.com/paper/2505.24781/) (2025)

## Abstract (arXiv)

A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are investigated, such as affine equivariance and breakdown value. The performance of the proposal is illustrated through the comparison to other techniques from the literature, in a simulation study and with a real dataset. The behavior when the underlying distribution is heavy-tailed or skewed, shows the appropriateness of the method when we deviate from the common assumption of normality. The resulting high correct detection rates and low false detection rates in the vast majority of cases, as well as the significantly smaller computation time shows the advantages of our proposal.