Tail bounds via generic chaining

Sjoerd Dirksen

doi:10.1214/EJP.v20-3760

Tail bounds via generic chaining

Sjoerd Dirksen

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Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.

Original language	English
Pages (from-to)	1-29
Journal	Electronic Journal of Probability
Volume	20
Issue number	53
DOIs	https://doi.org/10.1214/EJP.v20-3760
Publication status	Published - 20 May 2015
Externally published	Yes

Keywords

chaos processes
Deviation inequalities
generic chaining
restricted isometry property
suprema of empirical processes

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10.1214/EJP.v20-3760Licence: CC BY

EJP.v20-3760Final published version, 424 KBLicence: CC BY

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AB - We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process. These bounds lead to an estimate for the upper tail of the supremum with optimal deviation parameters. We apply our procedure to improve and extend some known deviation inequalities for suprema of unbounded empirical processes and chaos processes. As an application we give a significantly simplified proof of the restricted isometry property of the subsampled discrete Fourier transform.

KW - chaos processes

KW - Deviation inequalities

KW - generic chaining

KW - restricted isometry property

KW - suprema of empirical processes

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DO - 10.1214/EJP.v20-3760

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JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

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Tail bounds via generic chaining

Abstract

Keywords

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