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

Ori Davidov and George Iliopoulos

Journal of Nonparametric Statistics, 2012, vol. 24, issue 4, 923-933

Abstract: 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.

Date: 2012
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DOI: 10.1080/10485252.2012.710333

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