The Annals of Statistics

Testing for Spherical Symmetry of a Multivariate Distribution

Ludwig Baringhaus

Full-text: Open access

Abstract

Rotationally invariant tests based on test statistics of the 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 distribution 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.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 899-917.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348127

Digital Object Identifier
doi:10.1214/aos/1176348127

Mathematical Reviews number (MathSciNet)
MR1105851

Zentralblatt MATH identifier
0725.62053

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62H15: Hypothesis testing 33A50 33A65

Keywords
Invariant tests of spherical symmetry Gegenbauer polynomials

Citation

Baringhaus, Ludwig. Testing for Spherical Symmetry of a Multivariate Distribution. Ann. Statist. 19 (1991), no. 2, 899--917. doi:10.1214/aos/1176348127. https://projecteuclid.org/euclid.aos/1176348127


Export citation