## Institute of Mathematical Statistics Lecture Notes - Monograph Series

- Lecture Notes--Monograph Series
- Volume 55, 2007, 196-203

### A note on Talagrand’s convex hull concentration inequality

#### 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***Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom* (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007)

**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