Validity of the expected Euler characteristic heuristic
Jonathan Taylor, Akimichi Takemura, and Robert J. Adler
Source: Ann. Probab. Volume 33, Number 4 (2005), 1362-1396.
Abstract
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 fx, derived from the original process f.
Primary Subjects: 60G15, 60G60, 53A17, 58A05
Secondary Subjects: 60G17, 62M40, 60G70
Keywords: Random fields; Gaussian processes; manifolds; Euler characteristic; excursions; point processes; volume of tubes
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1120224584
Digital Object Identifier: doi:10.1214/009117905000000099
Mathematical Reviews number (MathSciNet):
MR2150192
Zentralblatt MATH identifier:
1083.60031
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