A note on Talagrand’s convex hull concentration inequality
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Institute of Mathematical Statistics Lecture Notes - Monograph Series

A note on Talagrand’s convex hull concentration inequality

David Pollard

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.

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.

Primary Subjects: 62E20
Secondary Subjects: 60F05, 62G08, 62G20
Keywords: Concentration of measure; convex hull; convexity

Full-text: Access granted (open access)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196797077
Digital Object Identifier: doi:10.1214/074921707000000364

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2008 © Institute of Mathematical Statistics

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Institute of Mathematical Statistics Lecture Notes - Monograph Series