The distribution of maxima of approximately Gaussian random fields
Yuval Nardi, David O. Siegmund, Benjamin Yakir
The Annals of Statistics · 2008 · Volume 36 · Issue 3
Abstract
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.
Keywords
60G15, 60G60, 60G70, asymptotically Gaussian, Extreme values, Random fields
Enable JavaScript for citation tools and additional paper interactions.