Confidence intervals for sparse precision matrix estimation via Lasso penalized D-trace loss

摘要

This article aims at establishing the confidence intervals for individual parameters of high-dimensional sparse precision matrix. Benefit from a precision matrix estimator which is defined as the minimizer of the Lasso penalized D-trace loss under a positive-definiteness constraint, we modify the KKT condition of the optimization problem to obtain a de-sparsified estimator. We analyze the asymptotic properties of the estimator under some regularity conditions and establish the asymptotic normality and confidence intervals for the case of sub-Gaussian observations. Numerical results show the performance of the proposed method.