The distribution of maxima of approximately Gaussian random fields

• 成果类型: Article
• 署名作者: Nardi, Yuval; Siegmund, David O.; Yakir, Benjamin
• 署名单位: Carnegie Mellon University; Stanford University; Hebrew University of Jerusalem
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS511
• 发表日期: 2008
• 页码: 1375-1403
• 关键词: tail probabilities

摘要

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.