The distribution of maxima of approximately Gaussian random fields

Yuval Nardi*, David O. Siegmund, Benjamin Yakir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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.

Original languageAmerican English
Pages (from-to)1375-1403
Number of pages29
JournalAnnals of Statistics
Volume36
Issue number3
DOIs
StatePublished - Jun 2008

Keywords

  • Asymptotically Gaussian
  • Extreme values
  • Random fields

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