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December, 1993 The Expected Number of Local Maxima of a Random Field and the Volume of Tubes
David Siegmund, Heping Zhang
Ann. Statist. 21(4): 1948-1966 (December, 1993). DOI: 10.1214/aos/1176349404

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.

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David Siegmund. Heping Zhang. "The Expected Number of Local Maxima of a Random Field and the Volume of Tubes." Ann. Statist. 21 (4) 1948 - 1966, December, 1993. https://doi.org/10.1214/aos/1176349404

Information

Published: December, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0801.62087
MathSciNet: MR1245775
Digital Object Identifier: 10.1214/aos/1176349404

Subjects:
Primary: 62J02
Secondary: 53A07

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 4 • December, 1993
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