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

Abstract

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.

Citation

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Yuri Golubev. "Adaptive spectral regularizations of high dimensional linear models." Electron. J. Statist. 5 1588 - 1617, 2011. https://doi.org/10.1214/11-EJS649

Information

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

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

Subjects:
Primary: 62C10
Secondary: 62G05

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

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