A fast and accurate kernel-based independence test with applications to high-dimensional and functional data

TL;DR

This paper introduces a new HSIC-based independence test that is fast, accurate, and applicable to high-dimensional and functional data, with proven asymptotic properties and superior performance in simulations and real data.

Contribution

A novel HSIC-based independence test with asymptotic null and alternative distributions, suitable for diverse data types, and demonstrating improved accuracy and efficiency.

Findings

Outperforms existing tests in level accuracy and power

Applicable to multivariate, high-dimensional, and functional data

Demonstrates efficiency through simulations and real data applications

Abstract

Testing the dependency between two random variables is an important inference problem in statistics since many statistical procedures rely on the assumption that the two samples are independent. To test whether two samples are independent, a so-called HSIC (Hilbert--Schmidt Independence Criterion)-based test has been proposed. Its null distribution is approximated either by permutation or a Gamma approximation. In this paper, a new HSIC-based test is proposed. Its asymptotic null and alternative distributions are established. It is shown that the proposed test is root-n consistent. A three-cumulant matched chi-squared approximation is adopted to approximate the null distribution of the test statistic. By choosing a proper reproducing kernel, the proposed test can be applied to many different types of data including multivariate, high-dimensional, and functional data. Three simulation studies and two real data applications show that in terms of level accuracy, power, and computational cost, the proposed test outperforms several existing tests for multivariate, high-dimensional, and functional data.