Nonparametric independence tests and k-sample tests for large sample sizes using package HHG

Abstract

Nonparametric tests of independence and k-sample tests are ubiquitous in modern applications, but they are typically computationally expensive. We present a family of nonparametric tests that are computationally efficient and powerful for detecting any type of dependence between a pair of univariate random variables. The computational complexity of the suggested tests is sub-quadratic in sample size, allowing calculation of test statistics for millions of observations. We survey both algorithms and the HHG package in which they are implemented, with usage examples showing the implementation of the proposed tests for both the independence case and the k-sample problem. The tests are compared to existing nonparametric tests via several simulation studies comparing both runtime and power. Special focus is given to the design of data structures used in implementation of the tests. These data structures can be useful for developers of nonparametric distribution-free tests.