THE EXPECTED NUMBER OF LOCAL MAXIMA OF A RANDOM-FIELD AND THE VOLUME OF TUBES

• 成果类型: Article
• 署名作者: SIEGMUND, D; ZHANG, HP
• 署名单位: Yale University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349404
• 发表日期: 1993
• 页码: 1948-1966
• 关键词: regression; parameter; inference; THEOREM

摘要

Using an expression for the expected number of local maxima of a random field, we derive an upper bound for the volume of a tube about a manifold in the unit sphere and show that under certain conditions our bound agrees with the evaluation of the tube volume in Weyl's formula. Applications to tests and confidence regions in nonlinear regression are discussed.