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December, 1983 Sobolev Tests for Symmetry of Directional Data
P. E. Jupp, B. D. Spurr
Ann. Statist. 11(4): 1225-1231 (December, 1983). DOI: 10.1214/aos/1176346335

Abstract

For testing a probability distribution on a compact Riemannian manifold for symmetry under the action of a given group of isometries, two classes of invariant tests are proposed and some properties noted. These tests are based on Sobolev norms and generalize Gine's Sobolev tests of uniformity. For general compact manifolds randomization tests analogous to Wellner's tests for the two-sample case are suggested. For the circle, distribution-free tests of symmetry based on uniform scores are provided.

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P. E. Jupp. B. D. Spurr. "Sobolev Tests for Symmetry of Directional Data." Ann. Statist. 11 (4) 1225 - 1231, December, 1983. https://doi.org/10.1214/aos/1176346335

Information

Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0551.62035
MathSciNet: MR720267
Digital Object Identifier: 10.1214/aos/1176346335

Subjects:
Primary: 62H15
Secondary: 62E20, 62G10

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 4 • December, 1983
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