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Rank-Based Inference for Multivariate Data in Factorial Designs

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Robust Rank-Based and Nonparametric Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 168))

Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Salzburg, 5020, Salzburg, Austria

    Arne C. Bathke

  2. Department of Statistics, University of Kentucky, Lexington, KY, 40536, USA

    Arne C. Bathke & Solomon W. Harrar

Authors
  1. Arne C. Bathke
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  2. Solomon W. Harrar
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Corresponding author

Correspondence to Arne C. Bathke .

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Editors and Affiliations

  1. Department of Statistics, Rutgers University, New Brunswick, New Jersey, USA

    Regina Y. Liu

  2. Department Statistics, Western Michigan University, Kalamazoo, Michigan, USA

    Joseph W. McKean

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Bathke, A.C., Harrar, S.W. (2016). Rank-Based Inference for Multivariate Data in Factorial Designs. In: Liu, R., McKean, J. (eds) Robust Rank-Based and Nonparametric Methods. Springer Proceedings in Mathematics & Statistics, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-319-39065-9_7

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