Two-Sample Test with Copula Entropy

TL;DR

This paper introduces a new non-parametric two-sample test based on copula entropy, demonstrating its effectiveness and competitive performance through simulation experiments on bi-variate data.

Contribution

It proposes a novel two-sample test using copula entropy with a non-parametric, hyperparameter-free estimator, improving testing performance on multivariate data.

Findings

The test performs well on simulated bi-variate normal and Gaussian copula data.

It outperforms or matches existing multivariate non-parametric tests.

The estimator is non-parametric and hyperparameter-free.

Abstract

In this paper we propose a two-sample test based on copula entropy (CE). The proposed test statistic is defined as the difference between the CEs of the null hypothesis and the alternative. The estimator of the test statistic is proposed with the non-parametric estimator of CE, which is non-parametric and hyperparameter-free. Simulation experiments verified the effectiveness of the proposed test and compared it with three other multivariate non-parametric two-sample tests on the simulated bi-variate normal or bi-variate Gaussian copula data. Experimental results show that the proposed test works well on all three simulations and presents competitive or better performance than the other three tests.