A novel robust estimation for high-dimensional precision matrices.

Abstract

In this paper we propose a new robust estimation of precision matrices for high-dimensional data when the number of variables is larger than the sample size. Different from the existing methods in literature, the proposed model combines the technique of modified Cholesky decomposition (MCD) with the robust generalized M-estimators. The MCD reparameterizes a precision matrix and transforms its estimation into solving a series of linear regressions, in which the commonly used robust techniques can be conveniently incorporated. Additionally, the proposed method adopts the model averaging idea to address the ordering issue in the MCD approach, resulting in an accurate estimation for precision matrices. Simulations and real data analysis are conducted to illustrate the merits of the proposed estimator.