In this paper, composite high-dimensional nonparametric tests for two samples are proposed, by using component-wise Wilcoxon–Mann–Whitney-type statistics. No distributional assumption, moment condition, or parametric model is required for the development of the tests and the theoretical results. Two approaches are employed, for estimating the asymptotic variance of the composite statistic, leading to two tests. In both cases, banding of the covariance matrix to estimate variance of the test statistic is involved. An adaptive algorithm, for selecting the banding window width, is proposed. Numerical studies are provided, to show the favorable performance of the new tests in finite samples and under varying degrees of dependence.
Bibliographical noteFunding Information:
The authors are grateful to the four anonymous referees, for critically reading the original version of the manuscript and making valuable suggestions that led to great improvements. The authors are, also, thankful to the editor for the orderly handling of the manuscript.
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.
- high dimension
- two-sample test
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- Chemistry (miscellaneous)
- Mathematics (all)
- Physics and Astronomy (miscellaneous)