Robust graphical lasso based on multivariate Winsorization

TL;DR

This paper introduces a robust graphical lasso method using multivariate Winsorization for sparse precision matrix estimation in Gaussian graphical models, demonstrating high robustness and competitive performance.

Contribution

It presents a novel robust covariance estimator based on multivariate Winsorization within the graphical lasso framework, achieving a high breakdown point and improved robustness.

Findings

The proposed estimator attains a breakdown point of 0.5 under cellwise contamination.

It shows competitive performance in precision matrix estimation and graph recovery.

Application to breast cancer data demonstrates practical usefulness.

Abstract

We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr-Muller-Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux-Ollerer's precision matrix estimator, our proposed estimator attains the maximum finite sample breakdown point of 0.5 under cellwise contamination. We conduct an extensive Monte Carlo simulation study to assess the performance of ours and the currently existing proposals. We find that ours has a competitive behavior, regarding the the estimation of the precision matrix and the recovery of the graph. We demonstrate the usefulness of the proposed methodology in a real application to breast cancer data.