## Bernoulli

• Bernoulli
• Volume 20, Number 4 (2014), 2020-2038.

### New concentration inequalities for suprema of empirical processes

#### Abstract

While effective concentration inequalities for suprema of empirical processes exist under boundedness or strict tail assumptions, no comparable results have been available under considerably weaker assumptions. In this paper, we derive concentration inequalities assuming only low moments for an envelope of the empirical process. These concentration inequalities are beneficial even when the envelope is much larger than the single functions under consideration.

#### Article information

Source
Bernoulli, Volume 20, Number 4 (2014), 2020-2038.

Dates
First available in Project Euclid: 19 September 2014

https://projecteuclid.org/euclid.bj/1411134452

Digital Object Identifier
doi:10.3150/13-BEJ549

Mathematical Reviews number (MathSciNet)
MR3263097

Zentralblatt MATH identifier
1355.60026

#### Citation

Lederer, Johannes; van de Geer, Sara. New concentration inequalities for suprema of empirical processes. Bernoulli 20 (2014), no. 4, 2020--2038. doi:10.3150/13-BEJ549. https://projecteuclid.org/euclid.bj/1411134452

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