Bernoulli

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

New concentration inequalities for suprema of empirical processes

Johannes Lederer and Sara van de Geer

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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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1411134452

Digital Object Identifier
doi:10.3150/13-BEJ549

Mathematical Reviews number (MathSciNet)
MR3263097

Zentralblatt MATH identifier
1355.60026

Keywords
chaining concentration inequalities deviation inequalities empirical processes rate of convergence

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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