High-Breakdown Robust Multivariate Methods

TL;DR

This paper reviews high-breakdown robust multivariate statistical methods that effectively handle substantial outliers, ensuring reliable analysis in complex data scenarios.

Contribution

It provides an overview of recent high-breakdown methods across various multivariate statistical techniques, highlighting their robustness against outliers.

Findings

High-breakdown methods can tolerate a large fraction of outliers.

Robust covariance estimation improves multivariate analysis reliability.

Applications include regression, discriminant analysis, and principal components.

Abstract

When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that are robust against the possibility that one or several unannounced outliers may occur anywhere in the data. These methods then allow to detect outlying observations by their residuals from a robust fit. We focus on high-breakdown methods, which can deal with a substantial fraction of outliers in the data. We give an overview of recent high-breakdown robust methods for multivariate settings such as covariance estimation, multiple and multivariate regression, discriminant analysis, principal components and multivariate calibration.