On Non-Asymptotic Bounds for Estimation in Generalized Linear Models with Highly Correlated Design

We study a high-dimensional generalized linear model and penalized empirical risk minimization with ℓ₁ 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.

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Bibliographic Details
Published in:Lecture notes-monograph series 2007-01, Vol.55, p.121-134
Main Author: van de Geer, Sara A.
Format: Article
Language:English
Subjects:
Convexity
Empiricism
Entropy
Estimators
Generalized linear model
Mathematical constants
Mathematical functions
Mathematical inequalities
Random variables
Online Access:Get full text
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Description
Summary:We study a high-dimensional generalized linear model and penalized empirical risk minimization with ℓ₁ 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.
ISSN:0749-2170
DOI:10.1214/074921707000000319