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.
Publié le : 2008-06-15
Classification:
Extreme values,
asymptotically Gaussian,
random fields,
60G15,
60G60,
60G70
@article{1211819568,
author = {Nardi, Yuval and Siegmund, David O. and Yakir, Benjamin},
title = {The distribution of maxima of approximately Gaussian random fields},
journal = {Ann. Statist.},
volume = {36},
number = {1},
year = {2008},
pages = { 1375-1403},
language = {en},
url = {http://dml.mathdoc.fr/item/1211819568}
}
Nardi, Yuval; Siegmund, David O.; Yakir, Benjamin. The distribution of maxima of approximately Gaussian random fields. Ann. Statist., Tome 36 (2008) no. 1, pp. 1375-1403. http://gdmltest.u-ga.fr/item/1211819568/