Zhuang Weiwei, Li Yadong, Qiu Guoxin
International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, People's Republic of China.
School of Management, University of Science and Technology of China, Hefei, People's Republic of China.
J Appl Stat. 2021 Aug 17;49(15):3804-3822. doi: 10.1080/02664763.2021.1965966. eCollection 2022.
Stochastic dominance is usually used to rank random variables by comparing their distributions, so it is widely applied in economics and finance. In actual applications, complete stochastic dominance is too demanding to meet, so relaxation indexes of stochastic dominance have attracted more attention. The index, the biggest gap between two distributions, can be a measure of the degree of deviation from complete dominance. The traditional estimation method is to use the empirical distribution functions to estimate it. Considering the populations under comparison are generally of the same nature, we can link the populations through density ratio model under certain condition. Based on this model, we propose a new estimator and establish its statistical inference theory. Simulation results show that the proposed estimator substantially improves estimation efficiency and power of the tests and coverage probabilities satisfactorily match the confidence levels of the tests, which show the superiority of the proposed estimator. Finally we apply our method to a real example of the Chinese household incomes.
随机占优通常用于通过比较随机变量的分布来对其进行排序，因此在经济学和金融领域得到广泛应用。在实际应用中，完全随机占优要求过高难以满足，因此随机占优的松弛指标受到了更多关注。该指标作为两个分布之间的最大差距，可以衡量偏离完全占优的程度。传统的估计方法是使用经验分布函数来估计它。考虑到所比较的总体通常具有相同的性质，我们可以在一定条件下通过密度比模型将总体联系起来。基于该模型，我们提出了一种新的估计量并建立了其统计推断理论。模拟结果表明，所提出的估计量显著提高了估计效率和检验功效，并且覆盖概率与检验的置信水平匹配良好，这表明了所提出估计量的优越性。最后，我们将我们的方法应用于中国家庭收入的一个实际例子。
