New tests for stochastic order with application to case control studies

Ori Davidov, Amir Herman

Research output: Contribution to journalArticlepeer-review


It is shown that if a binary regression function is increasing then retrospective sampling induces a stochastic ordering of the covariate distributions among the responders, which we call cases, and the non-responders, which we call controls. We also show that if the covariate distributions are stochastically ordered then the regression function must be increasing. This means that testing whether the regression function is monotone is equivalent to testing whether the covariate distributions are stochastically ordered. Capitalizing on these new probabilistic observations we proceed to develop two new non-parametric tests for stochastic order. The new tests are based on either the maximally selected, or integrated, chi-bar statistic of order one. The tests are easy to compute and interpret and their large sampling distributions are easily found. Numerical comparisons show that they compare favorably with existing methods in both small and large samples. We emphasize that the new tests are applicable to any testing problem involving two stochastically ordered distributions.

Original languageEnglish
Pages (from-to)2614-2623
Number of pages10
JournalJournal of Statistical Planning and Inference
Issue number8
StatePublished - 1 Aug 2009

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation Grant no. 1049/06.


  • Binary regression
  • Case-control studies
  • Chi-bar statistics
  • Order restricted statistical inference
  • Stochastic ordering

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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