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

## TL;DR

This paper introduces a robust multivariate outlier detection method using shrinkage estimators for Mahalanobis distance, demonstrating improved accuracy and efficiency over existing techniques, especially with non-normal data.

## Contribution

The paper proposes a novel robust Mahalanobis distance approach based on shrinkage estimators, with properties like affine equivariance and high computational efficiency.

## Key findings

- High correct detection rates in simulations
- Low false detection rates across datasets
- Reduced computation time compared to existing methods

## Abstract

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.