Estimating a distribution function subject to a stochastic order restriction: A comparative study

Ori Davidov, George Iliopoulos

Research output: Contribution to journalArticlepeer-review


In this article, we compare four nonparametric estimators of a distribution function (DF), estimated under a stochastic order restriction. The estimators are compared by simulation using four criteria: (1) the estimation of cumulative DFs; (2) the estimation of quantiles; (3) the estimation of moments and other functionals; and (4) as tools for testing for stochastic order. Our simulation study shows that estimators based on the pointwise maximum-likelihood estimator (p-MLE) outperform all other estimators when the underlying distributions are 'close' to each other. The gain in efficiency may be as high as 25%. If the DFs are far apart then the p-MLE may not be the best. However, the efficiency loss using the p-MLE relative to the best estimator in each case is generally low (about 5%). We also find that the test based on the p-MLE is the most powerful in the majority of cases although the gain in power relative to other tests is generally small.

Original languageEnglish
Pages (from-to)923-933
Number of pages11
JournalJournal of Nonparametric Statistics
Issue number4
StatePublished - Dec 2012

Bibliographical note

Funding Information:
The research of Ori Davidov was partially supported by the Israeli Science Foundation Grant No. 875/09.


  • empirical distribution function
  • nonparametric estimation
  • order restricted inference
  • rank tests
  • usual stochastic order

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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