Confidence intervals for high-dimensional inverse covariance estimation. Janková, J. & Geer, S. v. d. Electronic Journal of Statistics, 9(1):1205–1229, January, 2015. Publisher: Institute of Mathematical Statistics and Bernoulli Society![Confidence intervals for high-dimensional inverse covariance estimation [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex 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.
@article{jankova_confidence_2015,
title = {Confidence intervals for high-dimensional inverse covariance estimation},
volume = {9},
issn = {1935-7524, 1935-7524},
url = {https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-9/issue-1/Confidence-intervals-for-high-dimensional-inverse-covariance-estimation/10.1214/15-EJS1031.full},
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.},
number = {1},
urldate = {2024-05-29},
journal = {Electronic Journal of Statistics},
author = {Janková, Jana and Geer, Sara van de},
month = jan,
year = {2015},
note = {Publisher: Institute of Mathematical Statistics and Bernoulli Society},
keywords = {62F12, 62J07, Sparsity, confidence intervals, graphical lasso, high-dimensional, precision matrix},
pages = {1205--1229},
}
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