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Robust and Sparse Estimation of Graphical Models Based on Multivariate Winsorization

In: Robust and Multivariate Statistical Methods

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ginette Lafit & Javier Nogales & Marcelo Ruiz & Ruben Zamar, 2023. "Robust and Sparse Estimation of Graphical Models Based on Multivariate Winsorization," Springer Books, in: Mengxi Yi & Klaus Nordhausen (ed.), Robust and Multivariate Statistical Methods, pages 249-275, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-22687-8_12
    DOI: 10.1007/978-3-031-22687-8_12
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