Electronic Journal of Probability

Tail bounds via generic chaining

Sjoerd Dirksen

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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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 53, 29 pp.

Dates
Accepted: 20 May 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067159

Digital Object Identifier
doi:10.1214/EJP.v20-3760

Mathematical Reviews number (MathSciNet)
MR3354613

Zentralblatt MATH identifier
1327.60048

Keywords
Generic chaining deviation inequalities suprema of empirical processes restricted isometry property chaos processes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Dirksen, Sjoerd. Tail bounds via generic chaining. Electron. J. Probab. 20 (2015), paper no. 53, 29 pp. doi:10.1214/EJP.v20-3760. https://projecteuclid.org/euclid.ejp/1465067159


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