The Annals of Probability

Validity of the expected Euler characteristic heuristic

Jonathan Taylor, Akimichi Takemura, and Robert J. Adler

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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.

Article information

Source
Ann. Probab., Volume 33, Number 4 (2005), 1362-1396.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1120224584

Digital Object Identifier
doi:10.1214/009117905000000099

Mathematical Reviews number (MathSciNet)
MR2150192

Zentralblatt MATH identifier
1083.60031

Subjects
Primary: 60G15: Gaussian processes 60G60: Random fields 53A17: Kinematics 58A05: Differentiable manifolds, foundations
Secondary: 60G17: Sample path properties 62M40: Random fields; image analysis 60G70: Extreme value theory; extremal processes

Keywords
Random fields Gaussian processes manifolds Euler characteristic excursions point processes volume of tubes

Citation

Taylor, Jonathan; Takemura, Akimichi; Adler, Robert J. Validity of the expected Euler characteristic heuristic. Ann. Probab. 33 (2005), no. 4, 1362--1396. doi:10.1214/009117905000000099. https://projecteuclid.org/euclid.aop/1120224584


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