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.

26 pages

References in corpus (5)

• Covariance regularization by thresholding
• Sparse permutation invariant covariance estimation
• High-dimensional variable selection
• Can one estimate the conditional distribution of post-model-selection estimators?
• Statistical Theory for High-Dimensional Models

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