Robust and Sparse Estimation of Graphical Models Based on Multivariate Winsorization

Ginette Lafit (), Javier Nogales (), Marcelo Ruiz () and Ruben Zamar ()
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Ginette Lafit: University of Leuven
Javier Nogales: Universidad Carlos III de Madrid
Marcelo Ruiz: Universidad Nacional de Río Cuarto
Ruben Zamar: University of British Columbia

A chapter in Robust and Multivariate Statistical Methods, 2023, pp 249-275 from Springer

Abstract: Abstract We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr–Müller–Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux–Öllerer’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 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.

Keywords: Gaussian graphical model; Precision matrix; Sparse robust estimation; Cellwise contamination; Winsorization (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-22687-8_12

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DOI: 10.1007/978-3-031-22687-8_12

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