Abstract
This paper develops an empirical likelihood approach to testing for the presence of uniform stochastic ordering (or hazard rate ordering) among univariate distributions based on independent random samples from each distribution. The proposed test statistic is formed by integrating a localized empirical likelihood statistic with respect to the empirical distribution of the pooled sample. The asymptotic null distribution of this test statistic is found to have a simple distribution-free representation in terms of standard Brownian motion. The approach is extended to the case of right-censored survival data via multiple imputation. Two applications are discussed: (1) uncensored survival time data of mice exposed to radiation, and (2) right-censored time-to-infection data from a human HIV vaccine trial comparing a placebo group with a vaccine group.
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Acknowledgments
The authors thank the associate editor and two referees for their helpful comments. The authors thank also Peter Gilbert for helpful advice on using data from the Step Study and Ørnulf Borgan for help in providing R code for the Tarone–Ware statistic. The work of Ian McKeague was partially supported by NIH Grant R01GM095722-01 and NSF Grant DMS-1307838 and the work of Hammou El Barmi was partially supported by The City University of New York through a PSC-CUNY Grant.
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El Barmi, H., McKeague, I.W. Testing for uniform stochastic ordering via empirical likelihood. Ann Inst Stat Math 68, 955–976 (2016). https://doi.org/10.1007/s10463-015-0523-z
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DOI: https://doi.org/10.1007/s10463-015-0523-z