Validity of the expected Euler characteristic heuristic
概率论
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0507442,
title = {Validity of the expected Euler characteristic heuristic},
author = {Jonathan Taylor and Akimichi Takemura and Robert J. Adler},
journal= {arXiv preprint arXiv:math/0507442},
year = {2007}
}
备注
Published 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)