Generalized Independence Test for Modern Data

TL;DR

This paper introduces a new independence test for high-dimensional data that captures complex relationships, demonstrating strong power and reliable error control, with practical application to biological data.

Contribution

A novel independence test statistic designed for high-dimensional data that effectively captures intricate dependencies and converges to a chi-squared distribution under null hypothesis.

Findings

Exhibits strong power across various alternatives in simulations.

Converges to chi-squared distribution under null, ensuring error control.

Successfully applied to genotype-tissue expression data.

Abstract

The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel test statistic that captures intricate relationships using similarity and dissimilarity information derived from the data. The statistic exhibits strong power across a broad range of alternatives for high-dimensional data, as demonstrated in extensive simulation studies. Under mild conditions, we show that the new test statistic converges to the $\chi^2_4$ distribution under the permutation null distribution, ensuring straightforward type I error control. Furthermore, our research advances the moment method in proving the joint asymptotic normality of multiple double-indexed permutation statistics. We showcase the practical utility of this new test with an application to the Genotype-Tissue Expression dataset, where it effectively measures associations between human tissues.