• 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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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.

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

First available in Project Euclid: 19 September 2014

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chaining concentration inequalities deviation inequalities empirical processes rate of convergence


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.

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