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Mathematics > Statistics Theory

arXiv:0710.5797 (math)
[Submitted on 31 Oct 2007 (v1), last revised 27 Jun 2008 (this version, v2)]

Title:The distribution of maxima of approximately Gaussian random fields

Authors:Yuval Nardi, David O. Siegmund, 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.
Comments: Published in at this http URL the Annals of Statistics (this http URL) by the Institute of Mathematical Statistics (this http URL)
Subjects: Statistics Theory (math.ST)
MSC classes: 60G15, 60G60, 60G70 (Primary)
Report number: IMS-AOS-AOS511
Cite as: arXiv:0710.5797 [math.ST]
  (or arXiv:0710.5797v2 [math.ST] for this version)
  https://doi.org/10.48550/arXiv.0710.5797
Journal reference: Annals of Statistics 2008, Vol. 36, No. 3, 1375-1403
Related DOI: https://doi.org/10.1214/07-AOS511

Submission history

From: Yuval Nardi [view email]
[v1] Wed, 31 Oct 2007 02:51:45 UTC (47 KB)
[v2] Fri, 27 Jun 2008 08:22:34 UTC (111 KB)
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