Abstract Quantile and quantile effect (QE) functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This article offers a simple, practical construction of simultaneous confidence bands for quantile and QE functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling methods for observed and counterfactual distributions, and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. We find that universal insurance coverage increases the number of doctor visits across the entire distribution, and that the racial test score gap is small at early ages but grows with age due to socio-economic factors especially at the top of the distribution. Supplementary materials (additional results, R package, replication files) for this article are available online.

中文翻译：

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离散结果的分位数和分位数效应函数的通用推理

摘要 分位数和分位数效应 (QE) 函数因其自然和直观的解释而成为描述性和因果分析的重要工具。这些函数的现有推理方法不适用于离散随机变量。本文为可能离散的随机变量的分位数和 QE 函数提供了一个简单实用的同时置信带构造。它基于分布函数的同时置信带的自然转换，这对于许多问题都很容易获得。该构造是通用的，不依赖于潜在问题的性质。它与用于观察和反事实分布的参数、半参数和非参数建模方法结合使用，并且不依赖于采样方案。我们应用我们的方法来描述保险覆盖对医疗保健利用的分布影响，并获得种族测试分数差距的分布分解。我们发现全民保险增加了整个分布的就诊次数，并且种族测试分数差距在早期很小，但由于社会经济因素，尤其是在分布的顶部，随着年龄的增长而增加。本文的补充材料（附加结果、R 包、复制文件）可在线获取。并且种族测试分数差距在早期很小，但由于社会经济因素，特别是在分布的顶部，随着年龄的增长而增加。本文的补充材料（附加结果、R 包、复制文件）可在线获取。并且种族测试分数差距在早期很小，但由于社会经济因素，特别是在分布的顶部，随着年龄的增长而增加。本文的补充材料（附加结果、R 包、复制文件）可在线获取。