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.
Bibliographical noteFunding 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