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

**Authors:** Elisa Cabana, Rosa E. Lillo, Henry Laniado  
**arXiv:** [1904.02596](https://arxiv.org/abs/1904.02596)  
**Date:** 2019-04-04  
**Summary page:** https://www.summarizepaper.com/en/paper/1904.02596v1/

## Key points

- Proposal of robust Mahalanobis distances for multivariate outlier detection based on shrinkage
- Optimal estimation of robust intensity and scaling factors to define the shrinkage
- Investigation of properties such as affine equivariance and breakdown value
- Comparison to other techniques through simulation studies and a real dataset, demonstrating high correct detection rates and low false detection rates in the vast majority of cases
- Significantly smaller computation time compared to other methods
- Appropriateness when deviating from normality assumptions, including heavy-tailed or skewed distributions
- Introduction of a new evaluation metric, F-score, which combines precision and recall measures
- Comprehensive approach to multivariate outlier detection using robust Mahalanobis distances with shrinkage estimators

## Summary

This paper proposes a collection of robust Mahalanobis distances for multivariate outlier detection based on the concept of shrinkage. The authors optimally estimate robust intensity and scaling factors to define the shrinkage and investigate properties such as affine equivariance and breakdown value. The proposed method is compared to other techniques from the literature through simulation studies and a real dataset, demonstrating its high correct detection rates and low false detection rates in the vast majority of cases. Additionally, the significantly smaller computation time highlights the advantages of this proposal. The study also explores how the proposed method behaves when underlying distributions are heavy-tailed or skewed, showing its appropriateness when deviating from normality assumptions. Furthermore, the authors introduce a new evaluation metric, F-score which combines precision and recall measures. Overall, this paper presents a comprehensive approach to multivariate outlier detection using robust Mahalanobis distances with shrinkage estimators. The results demonstrate its effectiveness in detecting outliers while being computationally efficient and appropriate for non-normal distributions.