密度比模型下高阶随机占优的假设检验

doi:10.52396/JUST-2021-0179

中国科学技术大学学报 ›› 2021, Vol. 51 ›› Issue (12): 868-878.DOI: 10.52396/JUST-2021-0179

密度比模型下高阶随机占优的假设检验

周杨¹, 邱国新², 庄玮玮^3*

1.中国科学技术大学管理学院,安徽合肥 230026;
2.安徽新华学院商学院,安徽合肥 230088;
3.中国科学技术大学管理学院国际金融研究院,安徽合肥 230601

收稿日期:2021-08-06 修回日期:2021-09-30 出版日期:2021-12-31 发布日期:2022-01-11
通讯作者: *E-mail:weizh@ustc.edu.cn

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

ZHOU Yang¹, QIU Guoxin², ZHUANG Weiwei^3*

1. School of Management, University of Science and Technology of China, Hefei 230026, China;
2. School of Business, Xinhua University of Anhui, Hefei 230088, China;
3. International Institute of Finance, School of Management, University of Science and Technology of China, Hefei 230061, China

Received:2021-08-06 Revised:2021-09-30 Online:2021-12-31 Published:2022-01-11
Contact: *E-mail: weizh@ustc.edu.cn

摘要/Abstract

摘要： 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.

关键词: 随机占优, 密度比模型, 自助法, 经验似然

Abstract: 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.

Key words: stochastic dominance, density ratio model, bootstrap test, empirical likelihood

中图分类号:

周杨, 邱国新, 庄玮玮. 密度比模型下高阶随机占优的假设检验[J]. 中国科学技术大学学报, 2021, 51(12): 868-878.

ZHOU Yang, QIU Guoxin, ZHUANG Weiwei. Statistical test for high order stochastic dominance under the density ratio model[J]. Journal of University of Science and Technology of China, 2021, 51(12): 868-878.

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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

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