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Title: A Revisit to Bai--Saranadasa's Two-Sample Test
Authors: Jin-Ting Zhang 
Tianming Zhu 
Keywords: Bai–Saranadasa's two-sample test
high-dimensional data
χ2-type mixtures
three-cumulant matched χ2-approximation
Issue Date: 24-Dec-2021
Publisher: Taylor & Francis
Citation: Jin-Ting Zhang, Tianming Zhu (2021-12-24). A Revisit to Bai--Saranadasa's Two-Sample Test. Journal of Nonparametric Statistics 34 (01) : 58-76. ScholarBank@NUS Repository.
Abstract: Bai–Saranadasa's two-sample test for high-dimensional data, namely BS-test, has been widely cited in the literature. However, it may not control the size well when the required conditions are not satisfied. In this paper, a revisit to the BS-test is conducted. It is shown that under some regularity conditions and the null hypothesis, the BS-test statistic and a chi-square-type mixture have the same limiting distribution. It is then natural to approximate the null distribution of the BS-test using that of the chi-square-type mixture, which is actually obtained from the BS-test statistic when the two high-dimensional samples are normally distributed. The resulting test is then referred to as a normal-reference test. Two simulation studies and a real data example demonstrate that in terms of size control, the proposed normal-reference test performs very well and it performs substantially better than the BS-test and three other existing competitors proposed in the literature.
Source Title: Journal of Nonparametric Statistics
ISSN: 1048-5252
DOI: 10.1080/10485252.2021.2015768
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