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Keywords = Welch–Satterthwaite χ2-approximation

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21 pages, 1490 KiB  
Article
Testing Equality of Several Distributions at High Dimensions: A Maximum-Mean-Discrepancy-Based Approach
by Zhi Peng Ong, Aixiang Andy Chen, Tianming Zhu and Jin-Ting Zhang
Mathematics 2023, 11(20), 4374; https://doi.org/10.3390/math11204374 - 21 Oct 2023
Viewed by 3020
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Advances of Functional and High-Dimensional Data Analysis)
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