On non-asymptotic bounds for estimation in generalized linear models with highly correlated design
Log in :: RSS/Atom Feeds
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

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.

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.

Primary Subjects: 62G08
Keywords: convex hull; convex loss; covering number; non-asymptotic bound; penalized M-estimation

Full-text: Access granted (open access)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196797072
Digital Object Identifier: doi:10.1214/074921707000000319

back to Table of Contents

2008 © Institute of Mathematical Statistics

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Institute of Mathematical Statistics Lecture Notes - Monograph Series