Rank-Based Inference for Multivariate Data in Factorial Designs

  • Arne C. BathkeEmail author
  • Solomon W. Harrar
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 168)


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.


Asymptotics Multivariate statistics Nonparametric method Ordinal data Rank test 



Dedicated to Joe McKean on the occasion of his 70th birthday.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Fachbereich MathematikUniversität SalzburgSalzburgAustria
  2. 2.Department of StatisticsUniversity of KentuckyLexingtonUSA

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