Validity of the expected Euler characteristic heuristic

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f^x, derived from the original process f.
Published at http://dx.doi.org/10.1214/009117905000000099 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Keywords

Probability, 60G15, 60G60, 53A17, 58A05 (Primary) 60G17, 62M40, 60G70. (Secondary)

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/75854

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0507442
 http://arxiv.org/abs/math/0507442
 Annals of Probability 2005, Vol. 33, No. 4, 1362-1396
 doi:10.1214/009117905000000099

Collections

arXiv