Validity of the expected Euler characteristic heuristic
Open Access
- 1 July 2005
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 33 (4) , 1362-1396
- https://doi.org/10.1214/009117905000000099
Abstract
We study the accuracy of the expected Euler characteristic approximation to thedistribution of the maximum of a smooth, centered, unit variance Gaussian processf . Using a point process representation of the error, valid for arbitrary smoothprocesses, we show that the error is in general exponentially smaller than any termsin the approximation. We also give a lower bound on this exponential rate of decayin terms of the maximal variance of a family of Gaussian processes f, derived from...Keywords
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