TESTING FOR SPHERICAL-SYMMETRY OF A MULTIVARIATE DISTRIBUTION

• 成果类型: Article
• 署名作者: BARINGHAUS, L
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348127
• 发表日期: 1991
• 页码: 899-917
• 关键词: directions

摘要

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 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.