Flexible independence testing for hyperspherical data: a kernel approach for vectors of different dimensions

Abstract

Spherical and hyperspherical data are frequently encountered across various applied research domains, highlighting the essential task of evaluating independence within such data structures. In this context, we investigate the properties of test statistics based on distance correlation measures originally developed for the energy distance, and we extend this concept to strongly negative definite kernel-based distances. A significant advantage of employing this method is its versatility across different forms of directional data, enabling the assessment of independence among vectors of varying types. The applicability of these tests is demonstrated by numerical experiments and using several real datasets.