Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

TL;DR

This paper introduces a new robust estimation method for multivariate location and scatter that effectively handles both cellwise and casewise outliers, especially in high-dimensional, small-sample datasets.

Contribution

It proposes a novel estimator designed to improve robustness against mixed outliers, addressing limitations of traditional methods that down-weight entire cases.

Findings

Enhanced robustness to cellwise outliers

Improved performance in high-dimensional, small-sample scenarios

Effective handling of mixed outlier types

Abstract

Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of variables and a relatively small number of cases are common place in modern statistical applications. In these cases global down-weighting of an entire case, as performed by traditional robust procedures, may lead to poor results. We highlight the need for a new generation of robust estimators that can efficiently deal with cellwise outliers and at the same time show good performance under casewise outliers.