Institute of Mathematical Statistics Lecture Notes - Monograph Series

A note on Talagrand’s convex hull concentration inequality

David Pollard

Full-text: Open access

Abstract

The paper reexamines an argument by Talagrand that leads to a remarkable exponential tail bound for the concentration of probability near a set. The main novelty is the replacement of a mysterious calculus inequality by an application of Jensen's inequality.

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), 196-203

Dates
First available in Project Euclid: 4 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196797077

Digital Object Identifier
doi:10.1214/074921707000000364

Mathematical Reviews number (MathSciNet)
MR2459940

Zentralblatt MATH identifier
1180.60018

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 60F05: Central limit and other weak theorems 62G08: Nonparametric regression 62G20: Asymptotic properties

Keywords
Concentration of measure convex hull convexity

Rights
Copyright © 2007, Institute of Mathematical Statistics

Citation

Pollard, David. A note on Talagrand’s convex hull concentration inequality. Asymptotics: Particles, Processes and Inverse Problems, 196--203, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000364. https://projecteuclid.org/euclid.lnms/1196797077


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