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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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.

Article information

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

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1211819568

Digital Object Identifier
doi:10.1214/07-AOS511

Mathematical Reviews number (MathSciNet)
MR2418661

Zentralblatt MATH identifier
1148.60029

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

Keywords
Extreme values asymptotically Gaussian random fields

Citation

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. https://projecteuclid.org/euclid.aos/1211819568


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