Testing independence for spherical and hyperspherical data: Kernel-based approach

Abstract

In diverse applied research areas, encountering spherical and hyperspherical data is common, highlighting the essential task of assessing in dependence within such data structures. In this context, some properties of test statistics that rely on distance correlation measures initially introduced for energy distance are presented, and their generalizations are based on strongly negative definite kernels. One significant advantage of this method is its versatility across different types of directional data, allowing for the examination of independence among vectors of varying characteristics. In addition, they are shown to be powerful compared to existing competitors.