Rank-based inference for multivariate data in factorial designs

Arne C. Bathke, Solomon W. Harrar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


We introduce fully nonparametric, rank-based test statistics for inference on multivariate data in factorial designs, and derive their asymptotic sampling distribution. The focus here is on the asymptotic setting where the number of levels of one factor tends to infinity, while the number of levels of the other factor, as well as the replication size per factor level combination, are fixed. The resulting test statistics can be calculated directly, they don’t involve any iterative computational procedures. To our knowledge, they provide the first viable approach to a fully nonparametric analysis of, for example, multivariate ordinal responses, or a mix of ordinal with other response variables, in a factorial design setting.

Original languageEnglish
Title of host publicationRobust Rank-Based and Nonparametric Methods - Selected, Revised, and Extended Contributions
EditorsJoseph W. McKean, Regina Y. Liu
Number of pages19
StatePublished - 2016
EventInternational Conference on Robust Rank-Based and Nonparametric Methods, 2015 - Kalamazoo, United States
Duration: Apr 9 2015Apr 10 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


ConferenceInternational Conference on Robust Rank-Based and Nonparametric Methods, 2015
Country/TerritoryUnited States


  • Asymptotics
  • Multivariate statistics
  • Nonparametric method
  • Ordinal data
  • Rank test

ASJC Scopus subject areas

  • Mathematics (all)


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