Robust Inference for Inverse Stochastic Dominance

The notion of inverse stochastic dominance is gaining increasing support in risk, inequality, and welfare analysis as a relevant criterion for ranking distributions, which is alternative to the standard stochastic dominance approach. Its implementation rests on comparisons of two distributions’ quantile functions, or of their multiple partial integrals, at fixed population proportions. This article develops a novel statistical inference model for inverse stochastic dominance that is based on the influence function approach. The proposed method allows model-free evaluations that are limitedly affected by contamination in the data. Asymptotic normality of the estimators allows to derive tests for the restrictions implied by various forms of inverse stochastic dominance. Monte Carlo experiments and an application promote the qualities of the influence function estimator when compared with alternative dominance criteria.

在风险、不平等与福利分析领域，逆随机占优（inverse stochastic dominance）作为一种可替代标准随机占优方法的分布排序相关准则，正得到愈发广泛的认可与应用。其实现路径基于固定总体比例下，对两个分布的分位数函数或其多重部分积分开展比较。本文基于影响函数（influence function）方法，构建了面向逆随机占优的全新统计推断模型。所提方法支持无模型评估，且受数据污染的影响程度有限。估计量的渐近正态性可用于推导各类逆随机占优形式所隐含约束的检验方法。蒙特卡洛（Monte Carlo）模拟实验与实际应用案例表明，相较于其他占优准则，基于影响函数的估计量具备更优异的综合性能。