Inference for Likelihood Ratio Ordering in the Two-Sample Problem
研究了在似然比排序约束下两个多项概率向量的最大似然估计，并推广到单变量分布情形，证明了估计量的强相合性，推导了检验两个离散分布相等的似然比统计量的渐近分布，最后用胰岛素剂量数据比较了该方法与其他随机排序检验。
Abstract We obtain the maximum likelihood estimators of two multinomial probability vectors under the constraint that they are likelihood ratio ordered. We extend this estimation approach to the case of two univariate distributions and show strong consistency of the estimators. We also derive and study the asymptotic distribution of the likelihood ratio statistic for testing the equality of two discrete probability distributions against the alternative that one distribution is greater than the other in the likelihood ratio ordering sense. Finally, we examine a data set pertaining to average daily insulin dose from the Boston Collaborative Drug Surveillance Program and compare our testing procedure to testing procedures for other stochastic orderings.