Confidence intervals for high-dimensional inverse covariance estimation (original) (raw)
2015 Confidence intervals for high-dimensional inverse covariance estimation
Jana Janková,Sara van de Geer
Electron. J. Statist. 9(1): 1205-1229 (2015). DOI: 10.1214/15-EJS1031
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.
Citation
Jana Janková. Sara van de Geer. "Confidence intervals for high-dimensional inverse covariance estimation." Electron. J. Statist. 9 (1) 1205 - 1229, 2015. https://doi.org/10.1214/15-EJS1031
Information
Received: 1 March 2014; Published: 2015
First available in Project Euclid: 1 June 2015
Digital Object Identifier: 10.1214/15-EJS1031
Subjects:
Primary: 62J07
Secondary: 62F12
Keywords: confidence intervals, graphical lasso, high-dimensional, precision matrix, Sparsity
Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society
Vol.9 • No. 1 • 2015
