密度比模型下高阶随机占优的假设检验

Statistical test for high order stochastic dominance under the density ratio model

在经济学、医学等领域,如何比较两个分布的占优关系一直是人们关注的话题.通常会比较平均值或中位数.然而,具有更高均值的总体可能并不是最优的选择,因为它也可能具有更大的方差.随机占优为这个问题提供了一个很好的解决方案.那么,如何检验两个分布之间的随机占优就值得讨论.本文研究了密度比模型下高阶随机优势的检验统计量.此外,给出了检验统计量的渐近性,并使用自助法获得p值从而做出决策.模拟结果表明本文提出的检验统计量具有较高的功效.

In economics,medicine and other fields,how to compare the dominance relations between two distributions has been widely discussed.Usually population means or medians are compared.However,the population with a higher mean may not be what we will choose,since it may also have a larger variance.Stochastic dominance proposes a good solution to this problem.Subsequently,how to test stochastic dominance relations between two distributions is worth discussing.In this paper,we develop the test statistic of high order stochastic dominance under the density ratio model.In addition,we provide the asymptotic properties of test statistic and use the bootstrap method to obtain p-values to make decisions.Furthermore,the simulation results show that the proposed test statistics have the high test power.