Honest confidence regions and optimality in high-dimensional precision matrix estimation
Open access
Datum
2017-03Typ
- Journal Article
Abstract
We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters p can be much larger than the sample size. We show that the novel estimator achieves minimax rates in supremum norm and the low-dimensional components of the estimator have a Gaussian limiting distribution. These results hold uniformly over the class of precision matrices with row sparsity of small order √n/ log p and spectrum uniformly bounded, under a sub-Gaussian tail assumption on the margins of the true underlying distribution. Consequently, our results lead to uniformly valid confidence regions for low-dimensional parameters of the precision matrix. Thresholding the estimator leads to variable selection without imposing irrepresentability conditions. The performance of the method is demonstrated in a simulation study and on real data. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000206094Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
TESTBand
Seiten / Artikelnummer
Verlag
SpringerThema
Precision matrix; Sparsity; Inference; Asymptotic normality; Confidence regionsOrganisationseinheit
03717 - van de Geer, Sara (emeritus) / van de Geer, Sara (emeritus)
Anmerkungen
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.