  Estimation of a precision matrix (i.e., inverse covariance matrix) is widely
used to exploit conditional independence among continuous variables. The
influence of abnormal observations is exacerbated in a high dimensional setting
as the dimensionality increases. In this work, we propose robust estimation of
the inverse covariance matrix based on an $l_1$ regularized objective function
with a weighted sample covariance matrix. The robustness of the proposed
objective function can be justified by a nonparametric technique of the
integrated squared error criterion. To address the non-convexity of the
objective function, we develop an efficient algorithm in a similar spirit of
majorization-minimization. Asymptotic consistency of the proposed estimator is
also established. The performance of the proposed method is compared with
several existing approaches via numerical simulations. We further demonstrate
the merits of the proposed method with application in genetic network
inference.
