Barmi Hammou El, McKeague Ian W
Department of Statistics and Computer Information Systems, Baruch College, The City University of New York, One Baruch Way, New York, NY 10010, USA.
Bernoulli (Andover). 2013;19(1):295-307. doi: 10.3150/11-BEJ393SUPP.
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.
本文基于来自每个分布的独立随机样本，开发了一种经验似然方法，用于检验单变量分布之间是否存在随机序。所提出的检验统计量是通过对合并样本的经验分布积分一个局部经验似然统计量而形成的。发现该检验统计量的渐近零分布在标准布朗桥过程方面具有简单的无分布表示。该方法用于比较罗马皇帝在不同历史时期（包括帝国的“兴衰”阶段）的统治时长。在一项模拟研究中，发现所提出检验的功效比由埃尔·巴尔米和慕克吉提出的竞争检验有显著提高。
