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

Authors
SIEGMUND D ZHANG HP
Citation
D. Siegmund et Hp. Zhang, THE EXPECTED NUMBER OF LOCAL MAXIMA OF A RANDOM-FIELD AND THE VOLUME OF TUBES, Annals of statistics, 21(4), 1993, pp. 1948-1966
Citations number
25
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Annals of statistics → ACNP
ISSN journal
00905364
Volume
21
Issue
4
Year of publication
1993
Pages
1948 - 1966
Database
ISI
SICI code
0090-5364(1993)21:4<1948:TENOLM>2.0.ZU;2-U
Abstract
Using an expression for the expected number of local maxima of a rando m field, we derive an upper bound for the volume of a tube about a man ifold in the unit sphere and show that under certain conditions our bo und agrees with the evaluation of the tube volume in Weyl's formula. A pplications to tests and confidence regions in nonlinear regression ar e discussed.