Validity of the expected Euler characteristic heuristic

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dc.creatorTaylor, Jonathan
dc.creatorTakemura, Akimichi
dc.creatorAdler, Robert J.
dc.date2005-07-21
dc.date.accessioned2026-07-07T05:21:53Z
dc.date.available2026-07-07T05:21:53Z
dc.descriptionWe 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/math/0507442
dc.identifierhttp://arxiv.org/abs/math/0507442
dc.identifierAnnals of Probability 2005, Vol. 33, No. 4, 1362-1396
dc.identifierdoi:10.1214/009117905000000099
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75854
dc.subjectProbability
dc.subject60G15, 60G60, 53A17, 58A05 (Primary) 60G17, 62M40, 60G70. (Secondary)
dc.titleValidity of the expected Euler characteristic heuristic
dc.typetext

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