×

zbMATH — the first resource for mathematics

Sobolev tests for symmetry of directional data. (English) Zbl 0551.62035
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 E. GinĂ©’s Sobolev tests of uniformity [ibid. 3, 1243-1266 (1975; Zbl 0322.62058)].
For general compact manifolds randomization tests analogous to J. A. Wellner’s tests for the two-sample case [ibid. 7, 929-943 (1979; Zbl 0417.62044)] are suggested. For the circle, distribution-free tests of symmetry based on uniform scores are provided.

MSC:
62H15 Hypothesis testing in multivariate analysis
62A01 Foundations and philosophical topics in statistics
62G10 Nonparametric hypothesis testing
53B21 Methods of local Riemannian geometry
PDF BibTeX XML Cite
Full Text: DOI