The Annals of Statistics

The Expected Number of Local Maxima of a Random Field and the Volume of Tubes

David Siegmund and Heping Zhang

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 21, Number 4 (1993), 1948-1966.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349404

Digital Object Identifier
doi:10.1214/aos/1176349404

Mathematical Reviews number (MathSciNet)
MR1245775

Zentralblatt MATH identifier
0801.62087

JSTOR
links.jstor.org

Subjects
Primary: 62J02: General nonlinear regression
Secondary: 53A07: Higher-dimensional and -codimensional surfaces in Euclidean n-space

Keywords
Tube volume nonlinear regression

Citation

Siegmund, David; Zhang, Heping. The Expected Number of Local Maxima of a Random Field and the Volume of Tubes. Ann. Statist. 21 (1993), no. 4, 1948--1966. doi:10.1214/aos/1176349404. https://projecteuclid.org/euclid.aos/1176349404


Export citation