The distribution of maxima of approximately Gaussian random fields

Details The distribution of maxima of approximately Gaussian random fields The distribution of maxima of approximately Gaussian random fields

2007-10-31

arxiv.org/abs/0710.5797v2

Annals of Statistics 2008, Vol. 36, No. 3, 1375-1403

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS511 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS511

Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an approximation for the tail of the distribution. For the motivating class of problems this gives approximately the significance level of the maximum score test. The method is based on an application of a likelihood-ratio-identity followed by approximations of local fields. Numerical examples illustrate the accuracy of the approximations.

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