Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 9, Issue 1, Pages 1205-1229Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/15-EJS1031
Keywords
Confidence intervals; graphical Lasso; high-dimensional; precision matrix; sparsity
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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.
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