Confidence intervals for high-dimensional inverse covariance estimation

Abstract

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.

arXiv comment26 pages

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Cited by in corpus (8)

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• SEMgraph: An R Package for Causal Network Analysis of High-Throughput Data with Structural Equation Models
• Efficient Distributed Estimation of Inverse Covariance Matrices
• De-biased graphical Lasso for high-frequency data
• High-Temperature Structure Detection in Ferromagnets
• Non-asymptotic error controlled sparse high dimensional precision matrix estimation