Validity of the expected Euler characteristic heuristic

Details Validity of the expected Euler characteristic heuristic Validity of the expected Euler characteristic heuristic

2005-07-21

arxiv.org/abs/math/0507442v1

Annals of Probability 2005, Vol. 33, No. 4, 1362-1396

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117905000000099 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117905000000099

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.

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