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May 2011 Discrepancy, chaining and subgaussian processes
Shahar Mendelson
Ann. Probab. 39(3): 985-1026 (May 2011). DOI: 10.1214/10-AOP575

Abstract

We show that for a typical coordinate projection of a subgaussian class of functions, the infimum over signs inf(εi) supfF|∑i=1kεif(Xi)| is asymptotically smaller than the expectation over signs as a function of the dimension k, if the canonical Gaussian process indexed by F is continuous. To that end, we establish a bound on the discrepancy of an arbitrary subset of ℝk using properties of the canonical Gaussian process the set indexes, and then obtain quantitative structural information on a typical coordinate projection of a subgaussian class.

Citation

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Shahar Mendelson. "Discrepancy, chaining and subgaussian processes." Ann. Probab. 39 (3) 985 - 1026, May 2011. https://doi.org/10.1214/10-AOP575

Information

Published: May 2011
First available in Project Euclid: 16 March 2011

zbMATH: 1226.60011
MathSciNet: MR2789581
Digital Object Identifier: 10.1214/10-AOP575

Subjects:
Primary: 60C05 , 60D05 , 60G15

Keywords: Discrepancy , generic chaining

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 3 • May 2011
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