Institute of Mathematical Statistics Lecture Notes - Monograph Series

On non-asymptotic bounds for estimation in generalized linear models with highly correlated design

Sara A. van de Geer

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Abstract

We study a high-dimensional generalized linear model and penalized empirical risk minimization with $\ell_1$ penalty. Our aim is to provide a non-trivial illustration that non-asymptotic bounds for the estimator can be obtained without relying on the chaining technique and/or the peeling device.

Chapter information

Source
Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner, eds., Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 121-134

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196797072

Digital Object Identifier
doi:10.1214/074921707000000319

Mathematical Reviews number (MathSciNet)
MR2459935

Zentralblatt MATH identifier
1176.62071

Subjects
Primary: 62G08: Nonparametric regression

Keywords
convex hull convex loss covering number non-asymptotic bound penalized M-estimation

Rights
Copyright © 2007, Institute of Mathematical Statistics

Citation

van de Geer, Sara A. On non-asymptotic bounds for estimation in generalized linear models with highly correlated design. Asymptotics: Particles, Processes and Inverse Problems, 121--134, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000319. https://projecteuclid.org/euclid.lnms/1196797072


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