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.
Publié le : 1991-06-14
Classification:
Invariant tests of spherical symmetry,
Gegenbauer polynomials,
62E20,
62H15,
33A50,
33A65
@article{1176348127,
author = {Baringhaus, Ludwig},
title = {Testing for Spherical Symmetry of a Multivariate Distribution},
journal = {Ann. Statist.},
volume = {19},
number = {1},
year = {1991},
pages = { 899-917},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348127}
}
Baringhaus, Ludwig. Testing for Spherical Symmetry of a Multivariate Distribution. Ann. Statist., Tome 19 (1991) no. 1, pp. 899-917. http://gdmltest.u-ga.fr/item/1176348127/