  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.
