  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.
