Testing Equality of Several Distributions at High Dimensions: A Maximum-Mean-Discrepancy-Based Approach

Zhi Peng Ong, Aixiang Andy Chen, Tianming Zhu and Jin-Ting Zhang ()
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Zhi Peng Ong: Department of Information Systems and Analytics, National University of Singapore, Singapore 117417, Singapore
Aixiang Andy Chen: School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
Tianming Zhu: National Institute of Education, Nanyang Technological University, Singapore 637616, Singapore
Jin-Ting Zhang: Department of Statistics and Data Science, National University of Singapore, Singapore 117546, Singapore

Mathematics, 2023, vol. 11, issue 20, 1-21

Abstract: With the development of modern data collection techniques, researchers often encounter high-dimensional data across various research fields. An important problem is to determine whether several groups of these high-dimensional data originate from the same population. To address this, this paper presents a novel k -sample test for equal distributions for high-dimensional data, utilizing the Maximum Mean Discrepancy (MMD). The test statistic is constructed using a V-statistic-based estimator of the squared MMD derived for several samples. The asymptotic null and alternative distributions of the test statistic are derived. To approximate the null distribution accurately, three simple methods are described. To evaluate the performance of the proposed test, two simulation studies and a real data example are presented, demonstrating the effectiveness and reliability of the test in practical applications.

Keywords: multi-sample test; hypothesis testing; parametric bootstrap; random permutation; Welch–Satterthwaite ? 2 -approximation; chi-squared-type mixtures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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