Honest confidence regions and optimality in high-dimensional precision matrix estimation
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Jana Janková [1] ; Sara van de Geer [1]
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[1] Swiss Federal Institute of Technology in Zurich
Swiss Federal Institute of Technology in Zurich
Zürich, Suiza
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 26, Nº. 1, 2017, págs. 143-162
- Idioma: inglés
- DOI: 10.1007/s11749-016-0503-5
- Texto completo no disponible (Saber más ...)
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Resumen
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−−√/logp 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.
