Ball: An R Package for Detecting Distribution Difference and Association in Metric Spaces

Abstract

The rapid development of modern technology has created many complex datasets in non-linear spaces, while most of the statistical hypothesis tests are only available in Euclidean or Hilbert spaces. To properly analyze the data with more complicated structures, efforts have been made to solve the fundamental test problems in more general spaces (Lyons 2013; Pan, Tian, Wang, and Zhang 2018; Pan, Wang, Zhang, Zhu, and Zhu 2020). In this paper, we introduce a publicly available R package Ball for the comparison of multiple distributions and the test of mutual independence in metric spaces, which extends the test procedures for the equality of two distributions (Pan et al. 2018) and the independence of two random objects (Pan et al. 2020). The Ball package is computationally efficient since several novel algorithms as well as engineering techniques are employed in speeding up the ball test procedures. Two real data analyses and diverse numerical studies have been performed, and the results certify that the Ball package can detect various distribution differences and complicated dependencies in complex datasets, e.g., directional data and symmetric positive definite matrix data.