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.
Highlights
With the advanced modern instruments such as the Doppler shift acoustic radar, functional magnetic resonance imaging apparatus, and Heidelberg retina tomograph device, a large number of complex datasets are being collected for contemporary scientific research
Ball: Statistical Inference in Metric Spaces via Ball Test Statistics are potentially useful for the progress of scientific research, their various and complicated structures challenge testing the equality of distributions and testing the mutual independence of random objects, two fundamental problems of statistical inference
The two problems are generally named as the K-sample test problem and the test of mutual independence problem, which we reconsider in general metric spaces here
Summary
With the advanced modern instruments such as the Doppler shift acoustic radar, functional magnetic resonance imaging (fMRI) apparatus, and Heidelberg retina tomograph device, a large number of complex datasets are being collected for contemporary scientific research. The Ball package contributes to the open-source statistical software community in the following aspects: (i) It provides the BD two-sample test and the BCOV independence test to R users; (ii) It implements several dedicated design algorithms to accelerate the BD two-sample test and the BCOV independence test; (iii) It provides three powerful K-sample BD test statistics and an efficient K-sample permutation test procedure to distinguish distributions in metric spaces; (iv) It extends the BCOV test statistic to detect the mutual dependence among complex random objects in metric spaces; (v) It supports several generic sure independence screening procedures which are capable of extracting important features associated with complex objects in metric spaces.
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