Multivariate Location and Scatter Matrix Estimation Under Cellwise and Casewise Contamination

TL;DR

This paper enhances robust multivariate location and scatter matrix estimation by introducing a bivariate filter, a new subsampling method, and a non-monotonic weight function, significantly improving performance under cellwise and casewise contamination.

Contribution

It proposes a modified two-step robust estimation procedure with a bivariate filter, a fast subsampling method, and a non-monotonic weight function, advancing robustness and scalability.

Findings

Outperforms existing methods in high-dimensional settings.

Shows improved robustness against cellwise and casewise outliers.

Demonstrates effectiveness through simulations and real data analysis.

Abstract

We consider the problem of multivariate location and scatter matrix estimation when the data contain cellwise and casewise outliers. Agostinelli et al. (2015) propose a two-step approach to deal with this problem: first, apply a univariate filter to remove cellwise outliers and second, apply a generalized S-estimator to downweight casewise outliers. We improve this proposal in three main directions. First, we introduce a consistent bivariate filter to be used in combination with the univariate filter in the first step. Second, we propose a new fast subsampling procedure to generate starting points for the generalized S-estimator in the second step. Third, we consider a non-monotonic weight function for the generalized S-estimator to better deal with casewise outliers in high dimension. A simulation study and real data example show that, unlike the original two-step procedure, the modified two-step approach performs and scales well for high dimension. Moreover, the modified procedure outperforms the original one and other state-of-the-art robust procedures under cellwise and casewise data contamination.