Ranking procedures for matched pairs with missing data Asymptotic theory and a small sample approximation

F. Konietschke, S. W. Harrar, K. Lange, E. Brunner

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


Nonparametric methods for matched pairs with data missing completely at random are considered. It is not assumed that the observations are coming from distribution functions belonging to a certain parametric or semi-parametric family. In particular, the distributions can have different shapes under the null hypothesis. Hence, the so-called nonparametric BehrensFisher problem for matched pairs with missing data is considered. Moreover, a new approach for confidence intervals for nonparametric effects is presented. In particular, no restriction on the ratio of the number of complete and incomplete cases is required to derive the asymptotic results. Simulations show that for arbitrary settings of complete data and missing values, the resulting confidence intervals maintain the pre-assigned coverage probability quite accurately. Regarding the power, none of the proposed tests is uniformly superior to the other. A real data set illustrates the application.

Original languageEnglish
Pages (from-to)1090-1102
Number of pages13
JournalComputational Statistics and Data Analysis
Issue number5
StatePublished - May 1 2012

Bibliographical note

Funding Information:
The authors are grateful to an Associate Editor and two anonymous referees for helpful comments which led to considerable improvement of the paper. We would like to thank Dr. Gao (York University, Canada) for making the data set available. This work was supported in part by the German Research Foundation Br-655/16-1 .


  • BehrensFisher problem
  • Missing values
  • Nonparametric hypothesis
  • Ordered categorical data
  • Rank test
  • Repeated measures design
  • Ties

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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