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Empirical likelihood-based tests for stochastic ordering. (English) Zbl 1259.62030

Summary: This paper develops an empirical likelihood approach to testing for the presence of stochastic orderings 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 bridge processes. The approach is used to compare the lengths of rules of Roman Emperors over various historical periods, including the “decline and fall” phase of the empire. In a simulation study, the power of the proposed test is found to improve substantially upon that of a competing test due to El Barmi and Mukerjee [J. Am. Stat. Assoc. 100, No. 469, 252–261 (2005; Zbl 1117.62326)].

MSC:

62G10 Nonparametric hypothesis testing
60E15 Inequalities; stochastic orderings
62G30 Order statistics; empirical distribution functions
62E20 Asymptotic distribution theory in statistics
62F30 Parametric inference under constraints
65C60 Computational problems in statistics (MSC2010)
91F10 History, political science

Citations:

Zbl 1117.62326
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References:

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