  The precision matrix that encodes conditional linear dependency relations
among a set of variables forms an important object of interest in multivariate
analysis. Sparse estimation procedures for precision matrices such as the
graphical lasso (Glasso) gained popularity as they facilitate interpretability,
thereby separating pairs of variables that are conditionally dependent from
those that are independent (given all other variables). Glasso lacks, however,
robustness to outliers. To overcome this problem, one typically applies a
robust plug-in procedure where the Glasso is computed from a robust covariance
estimate instead of the sample covariance, thereby providing protection against
outliers. In this paper, we study such estimators theoretically, by deriving
and comparing their influence function, sensitivity curves and asymptotic
variances.
