Open Access
2011 Adaptive spectral regularizations of high dimensional linear models
Yuri Golubev
Electron. J. Statist. 5: 1588-1617 (2011). DOI: 10.1214/11-EJS649


This paper focuses on recovering an unknown vector β from the noisy data Y=Xβ+σξ, where X is a known n×p-matrix, ξ is a standard white Gaussian noise, and σ is an unknown noise level. In order to estimate β, a spectral regularization method is used, and our goal is to choose its regularization parameter with the help of the data Y. In this paper, we deal solely with regularization methods based on the so-called ordered smoothers (see [13]) and extend the oracle inequality from [11] to the case, where the noise level is unknown.


Download Citation

Yuri Golubev. "Adaptive spectral regularizations of high dimensional linear models." Electron. J. Statist. 5 1588 - 1617, 2011.


Published: 2011
First available in Project Euclid: 23 November 2011

zbMATH: 1271.62146
MathSciNet: MR2861698
Digital Object Identifier: 10.1214/11-EJS649

Primary: 62C10
Secondary: 62G05

Keywords: empirical risk minimization , excess risk , Oracle inequality , ordered smoother , Spectral regularization

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

Back to Top