Generalized Nonparametric Composite Tests for High-Dimensional Data

Xiaoli Kong, Alejandro Villasante-Tezanos, Solomon W. Harrar

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number1153
JournalSymmetry
Volume14
Issue number6
DOIs
StatePublished - Jun 2022

Bibliographical note

Funding 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.

Publisher Copyright:
© 2022 by the authors. Licensee MDPI, Basel, Switzerland.

Keywords

  • high dimension
  • nonparametric
  • two-sample test
  • Wilcoxon–Mann–Whitney
  • α-mixing

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics (all)
  • Physics and Astronomy (miscellaneous)

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