Power of Tests of Uniformity Defined on the Hypersphere

Abstract

In multivariate data with n individuals described by p variables it is usual to assume that the variables are fixed and the individuals are randomly selected; in the present study we assume that the individuals are fixed and the previously normalised variables are randomly selected from a population of variables. When we want to associate to the sample of variables a distribution, like the Bingham distribution, it is important to use beforehand a test of uniformity. In this article, we compare the power of Bingham and Giné tests of uniformity for some dimensions of the sphere, vs. a Bingham population or a mixture of Bingham populations.

Keywords:

• Bingham distribution
• Directional data
• Selection of variables
• Tests of uniformity