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We analyze the statistical consistency of robust estimators for precisionmatrices in high dimensions. We focus on a contamination mechanism actingcellwise on the data matrix. The estimators we analyze are formed by pluggingappropriately chosen robust covariance matrix estimators into the graphicalLasso and CLIME. Such estimators were recently proposed in the robuststatistics literature, but only analyzed mathematically from the point of viewof the breakdown point. This paper provides complementary high-dimensionalerror bounds for the precision matrix estimators that reveal the interplaybetween the dimensionality of the problem and the degree of contaminationpermitted in the observed distribution. We also show that although thegraphical Lasso and CLIME estimators perform equally well from the point ofview of statistical consistency, the breakdown property of the graphical Lassois superior to that of CLIME. We discuss implications of our work for problemsinvolving graphical model estimation when the uncontaminated data follow amultivariate normal distribution, and the goal is to estimate the support ofthe population-level precision matrix. Our error bounds do not make anyassumptions about the the contaminating distribution and allow for anonvanishing fraction of cellwise contamination.

High-dimensional robust precision matrix estimation: Cellwise corruption under $\epsilon$-contamination