Parametric and nonparametric bootstrap methods for general MANOVA

Frank Konietschke, Arne C. Bathke, Solomon W. Harrar, Markus Pauly

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


We develop parametric and nonparametric bootstrap methods for multi-factor multivariate data, without assuming normality, and allowing for covariance matrices that are heterogeneous between groups. The newly proposed, general procedure includes several situations as special cases, such as the multivariate Behrens-Fisher problem, the multivariate one-way layout, as well as crossed and hierarchically nested two-way layouts. We derive the asymptotic distribution of the bootstrap tests for general factorial designs and evaluate their performance in an extensive comparative simulation study. For moderate sample sizes, the bootstrap approach provides an improvement to existing methods in particular for situations with nonnormal data and heterogeneous covariance matrices in unbalanced designs. For balanced designs, less computationally intensive alternatives based on approximate sampling distributions of multivariate tests can be recommended.

Original languageEnglish
Pages (from-to)291-301
Number of pages11
JournalJournal of Multivariate Analysis
StatePublished - Sep 1 2015

Bibliographical note

Funding Information:
The authors are grateful to an Associate Editor and two anonymous referees for helpful comments which considerably improved the paper. The authors would like to thank Edgar Brunner for helpful comments. This work was supported by the German Research Foundation project DFG-PA 2409/3-1 .

Publisher Copyright:
© 2015 Elsevier Inc..


  • Multivariate Behrens-Fisher problem
  • Multivariate data
  • Nonparametric bootstrap
  • Parametric bootstrap
  • Wald test

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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