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June, 1990 Hotelling's Theorem on the Volume of Tubes: Some Illustrations in Simultaneous Inference and Data Analysis
Soren Johansen, Iain M. Johnstone
Ann. Statist. 18(2): 652-684 (June, 1990). DOI: 10.1214/aos/1176347620

Abstract

We illustrate with contemporary examples Hotelling's geometric approach to simultaneous probability calculations. Hotelling reduces the evaluation of certain normal theory significance probabilities to finding the volume of a tube about a curve in a hypersphere, and shows that this volume is often exactly given by length times cross-sectional area. We review Hotelling's result together with some recent complements, and then use the approach to set simultaneous prediction regions for some data from gait analysis, to study Andrews' plots in multivariate data analysis, and to construct significance tests for projection pursuit regression. A by-product is a numerical criterion for tube self-overlap, relevant, for example, to uniqueness of certain nonlinear least squares estimates.

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Soren Johansen. Iain M. Johnstone. "Hotelling's Theorem on the Volume of Tubes: Some Illustrations in Simultaneous Inference and Data Analysis." Ann. Statist. 18 (2) 652 - 684, June, 1990. https://doi.org/10.1214/aos/1176347620

Information

Published: June, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0723.62018
MathSciNet: MR1056331
Digital Object Identifier: 10.1214/aos/1176347620

Subjects:
Primary: 62E15
Secondary: 62F25, 62J02, 62J15

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 2 • June, 1990
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