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

Article Type

Research Article

Publication Title

Test

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.

First Page

525

Last Page

547

DOI

10.1007/s11749-015-0467-x

Publication Date

9-1-2016

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