Empirical likelihood-based tests for stochastic ordering

TLDR: In this paper, an empirical likelihood approach to test for the presence of stochastic ordering among univariate distributions based on independent random samples from each distribution is proposed. But the approach is used to compare the lengths of rule of Roman Emperors over various historical periods, including the decline and fall of the empire.

Abstract: This paper develops an empirical likelihood approach to testing for the presence of stochastic 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 bridge processes. The approach is used to compare the lengths of rule 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.