We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian limiting distribution. Asymptotic properties of the novel estimator are analyzed for the case of sub-Gaussian observations under a sparsity assumption on the entries of the true precision matrix and regularity conditions. Thresholding the de-sparsified estimator gives guarantees for edge selection in the associated graphical model. Performance of the proposed method is illustrated in a simulation study.
"Confidence intervals for high-dimensional inverse covariance estimation." Electron. J. Statist. 9 (1) 1205 - 1229, 2015. https://doi.org/10.1214/15-EJS1031