Electronic Journal of Statistics

Adaptive spectral regularizations of high dimensional linear models

Yuri Golubev

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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.

Article information

Source
Electron. J. Statist., Volume 5 (2011), 1588-1617.

Dates
First available in Project Euclid: 23 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1322057437

Digital Object Identifier
doi:10.1214/11-EJS649

Mathematical Reviews number (MathSciNet)
MR2861698

Zentralblatt MATH identifier
1271.62146

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62G05: Estimation

Keywords
spectral regularization excess risk ordered smoother empirical risk minimization oracle inequality

Citation

Golubev, Yuri. Adaptive spectral regularizations of high dimensional linear models. Electron. J. Statist. 5 (2011), 1588--1617. doi:10.1214/11-EJS649. https://projecteuclid.org/euclid.ejs/1322057437


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