The Annals of Statistics

The distribution of maxima of approximately Gaussian random fields

Yuval Nardi, David O. Siegmund, and Benjamin Yakir

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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.

Article information

Ann. Statist., Volume 36, Number 3 (2008), 1375-1403.

First available in Project Euclid: 26 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G15: Gaussian processes 60G60: Random fields 60G70: Extreme value theory; extremal processes

Extreme values asymptotically Gaussian random fields


Nardi, Yuval; Siegmund, David O.; Yakir, Benjamin. The distribution of maxima of approximately Gaussian random fields. Ann. Statist. 36 (2008), no. 3, 1375--1403. doi:10.1214/07-AOS511.

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