Distribution-free high-dimensional two-sample tests based on discriminating hyperplanes

Anil K. Ghosh () and Munmun Biswas ()
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Anil K. Ghosh: Indian Statistical Institute
Munmun Biswas: Indian Statistical Institute

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 25, issue 3, No 7, 525-547

Abstract: Abstract In this article, we propose a general procedure for multivariate generalizations of univariate distribution-free tests involving two independent samples as well as matched pair data. This proposed procedure is based on ranks of real-valued linear functions of multivariate observations. The linear function used to rank the observations is obtained by solving a classification problem between the two multivariate distributions from which the observations are generated. Our proposed tests retain the distribution-free property of their univariate analogs, and they perform well for high-dimensional data even when the dimension exceeds the sample size. Asymptotic results on their power properties are derived when the dimension grows to infinity and the sample size may or may not grow with the dimension. We analyze several high-dimensional simulated and real data sets to compare the empirical performance of our proposed tests with several other tests available in the literature.

Keywords: Distance-weighted discrimination; Kolmogorov–Smirnov statistic; Sign test; Signed rank test; Support vector machines; Wilcoxon–Mann–Whitney statistic; 62G10; 62H15 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11749-015-0467-x

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