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Testing for spherical symmetry of a multivariate distribution. (English) Zbl 0725.62053

Summary: Rotationally invariant tests based on test statistics of von Mises type are proposed under the hypothesis of spherical symmetry of a multivariate distribution. The tests are distribution-free when the hypothesis of spherical symmetry is true. The asymptotic distributions of the test statistics are derived under the null hypothesis and under any fixed alternative. A simple criterion for consistency is given. The results are illustrated by numerous examples of test statistics which give rise to tests being consistent against all alternatives.

MSC:

62H15 Hypothesis testing in multivariate analysis
62E20 Asymptotic distribution theory in statistics
62A01 Foundations and philosophical topics in statistics
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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