Published August 2012
| Submitted
Journal Article
Open
Expected Supremum of a Random Linear Combination of Shifted Kernels
Abstract
We address the expected supremum of a linear combination of shifts of the sinc kernel with random coefficients. When the coefficients are Gaussian, the expected supremum is of order √log n, where n is the number of shifts. When the coefficients are uniformly bounded, the expected supremum is of order log log n. This is a noteworthy difference to orthonormal functions on the unit interval, where the expected supremum is of order √n log n for all reasonable coefficient statistics.
Additional Information
© 2012 Springer Science+Business Media, LLC. Received: 20 June 2011; Revised: 15 December 2011; Published online: 3 February 2012. H. Boche was supported by start-up funds of the Technische Universität München.Attached Files
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Additional details
- Eprint ID
- 35482
- Resolver ID
- CaltechAUTHORS:20121115-101446778
- Technische Universität München
- Created
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2012-11-21Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field