The Annals of Statistics

Sobolev Tests for Symmetry of Directional Data

P. E. Jupp and B. D. Spurr

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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.

Article information

Source
Ann. Statist., Volume 11, Number 4 (1983), 1225-1231.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346335

Digital Object Identifier
doi:10.1214/aos/1176346335

Mathematical Reviews number (MathSciNet)
MR720267

Zentralblatt MATH identifier
0551.62035

JSTOR
links.jstor.org

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62G10: Hypothesis testing 62E20: Asymptotic distribution theory

Keywords
Consistency directional data group action invariance randomization tests Riemannian manifolds symmetry uniform scores

Citation

Jupp, P. E.; Spurr, B. D. Sobolev Tests for Symmetry of Directional Data. Ann. Statist. 11 (1983), no. 4, 1225--1231. doi:10.1214/aos/1176346335. https://projecteuclid.org/euclid.aos/1176346335


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