Confidence intervals for high-dimensional inverse covariance estimation

In this paper, we establish confidence intervals for individual parameters of a sparse concentration matrix in a high-dimensional setting. We follow the idea of the projection approach proposed in \cite{vdgeer13}, which is applied to the graphical Lasso to obtain a de-sparsified estimator. Subsequently, we analyze the asymptotic properties of the novel estimator, establishing asymptotic normality and confidence intervals for the case of sub-Gaussian observations. Performance of the proposed method is illustrated in a simulation study.