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March, 1989 On Hotelling's Formula for the Volume of Tubes and Naiman's Inequality
Iain Johnstone, David Siegmund
Ann. Statist. 17(1): 184-194 (March, 1989). DOI: 10.1214/aos/1176347010

Abstract

Two new derivations of the Hotelling-Naiman results on the volume of tubes about curves in spheres are presented. The first involves simple differential inequalities. The second is probabilistic, using the concept of upcrossing borrowed from the theory of Gaussian processes. The upcrossings method is extended to an harmonic regression problem not covered by the Hotelling-Naiman formulation.

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Iain Johnstone. David Siegmund. "On Hotelling's Formula for the Volume of Tubes and Naiman's Inequality." Ann. Statist. 17 (1) 184 - 194, March, 1989. https://doi.org/10.1214/aos/1176347010

Information

Published: March, 1989
First available in Project Euclid: 12 April 2007

zbMATH: 0678.62066
MathSciNet: MR981444
Digital Object Identifier: 10.1214/aos/1176347010

Subjects:
Primary: 62E15
Secondary: 53A04

Keywords: differential inequalities , upcrossings

Rights: Copyright © 1989 Institute of Mathematical Statistics

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Vol.17 • No. 1 • March, 1989
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