Robust estimation of sparse precision matrix using adaptive weighted graphical lasso approach

Estimation of a precision matrix (i.e. inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence abnormal observations exacerbated in high dimensional setting as the dimensionality increases. In this work, we propose robust estimation based on an l1 regularised objective function with weighted sample matrix. robustness proposed can be justified by nonparametric technique integrated squared error criterion. To address non-convexity function, develop efficient algorithm similar spirit majorisation-minimisation. Asymptotic consistency estimator also established. performance method compared several existing approaches via numerical simulations. We further demonstrate merits application genetic network inference.