Consistent complete independence test in high dimensions based on Chatterjee correlation coefficient

TL;DR

This paper introduces new high-dimensional independence tests based on Chatterjee's correlation, including quadratic, extreme value, and power enhancement tests, with proven large sample properties and demonstrated effectiveness on synthetic and real data.

Contribution

It develops novel independence tests using Chatterjee's correlation, especially the power enhancement test that improves detection under sparse alternatives.

Findings

Proposed quadratic and extreme value tests with good performance.

Established large sample properties under null and alternative hypotheses.

Demonstrated effectiveness through synthetic and real data experiments.

Abstract

In this article, we consider the complete independence test of high-dimensional data. Based on Chatterjee coefficient, we pioneer the development of quadratic test and extreme value test which possess good testing performance for oscillatory data, and establish the corresponding large sample properties under both null hypotheses and alternative hypotheses. In order to overcome the shortcomings of quadratic statistic and extreme value statistic, we propose a testing method termed as power enhancement test by adding a screening statistic to the quadratic statistic. The proposed method do not reduce the testing power under dense alternative hypotheses, but can enhance the power significantly under sparse alternative hypotheses. Three synthetic data examples and two real data examples are further used to illustrate the performance of our proposed methods.