A0243
Title: A fast and accurate kernel-based independence test
Authors: Jin-Ting Zhang - National University of Singapore (Singapore)
Tianming Zhu - National Institute of Education, Nanyang Technological University (Singapore)
Jin-Ting Zhang - National University of Singapore (Singapore) [presenting]
Abstract: Testing the dependency between two random variables is a vital statistical inference problem since many statistical procedures rely on the assumption that the two samples are independent. A so-called HSIC (Hilbert-Schmidt Independence Criterion)-based test has been proposed to test whether two samples are independent. Its null distribution is approximated either by permutation or a Gamma approximation. Unfortunately, the permutation-based test is very time-consuming, and the Gamma-approximation-based test does not work well for high-dimensional data. 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. The proposed test can be applied to many different data types, including multivariate, high-dimensional, and functional data, by choosing a proper reproducing kernel. Three simulation studies and two real data applications show that the proposed test outperforms several tests for multivariate, high-dimensional, and functional data in terms of level accuracy, power, and computational cost.
