Understanding Spherical and Hyperspherical Data: From Association Measurement to Variable Selection

Abstract

Hyperspherical or directional data naturally arise in many different earth sciences, such as geology, seismology, astrophysics, oceanography, and meteorology, as well as in studies of animal behavior, proteomics, and neuroscience. However, the special structure of such data makes it quite challenging to identify associations, primarily due to the non-trivial adaptation of statistical methodologies designed for Euclidean data. Here, we present recent results in detecting dependence using generalized energy distance statistics and extend this methodology for application to variable screening in high-dimensional data cases.