2023/01/03 by Jin‐Ting Zhang, Zhang, Jin-Ting, Tianming Zhu +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Gene expression and cancer classification #Methodology (stat.ME) #Neural Networks and Applications #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2301.00967
openalex publication_date 2023/01/03 · openalex created_date 2023/01/06 · openalex updated_date 2026/07/28
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.