Hypothesis tests and sure independence screening (SIS) procedure based on ball
statistics, including ball divergence, ball covariance, and ball correlation <doi:10.1080/01621459.2018.1462709>,
are developed to analyze complex data. The ball divergence and ball covariance based distribution-free
tests are implemented to examine equality of multivariate distributions and independence
between random vectors of arbitrary dimensions. Furthermore, a generic non-parametric SIS
procedure based on ball correlation and all of its variants are implemented to tackle the
challenge in the context of ultra high dimensional data.

Xueqin Wang, Wenliang Pan, Heping Zhang, Hongtu Zhu, Yuan Tian, Weinan Xiao, Chengfeng Liu, Jin Zhu
Hypothesis tests and sure independence screening (SIS) procedure based on ball statistics, including ball divergence <doi:10.1214/17-AOS1579>, ball covariance, and ball correlation <doi:10.1080/01621459.2018.1462709>, are developed to analyze complex data. The ball divergence and ball covariance based distribution-free tests are implemented to examine equality of multivariate distributions and independence between random vectors of arbitrary dimensions. Furthermore, a generic non-parametric SIS procedure based on ball correlation and all of its variants are implemented to tackle the challenge in the context of ultra high dimensional data.

Xueqin Wang, Wenliang Pan, Heping Zhang, Hongtu Zhu, Yuan Tian, Weinan Xiao, Chengfeng Liu, Ruihuang Liu, Jin Zhu
Hypothesis tests and sure independence screening (SIS) procedure based on ball statistics, including ball divergence <doi:10.1214/17-AOS1579>, ball covariance <doi:10.1080/01621459.2018.1543600>, and ball correlation <doi:10.1080/01621459.2018.1462709>, are developed to analyze complex data in metric spaces, e.g, shape, directional, compositional and symmetric positive definite matrix data. The ball divergence and ball covariance based distribution-free tests are implemented to detecting distribution difference and association in metric spaces <arXiv:1811.03750>. Furthermore, several generic non-parametric feature selection procedures based on ball correlation, BCor-SIS and all of its variants, are implemented to tackle the challenge in the context of ultra high dimensional data.