Non‐parametric inference on (conditional) quantile differences and interquantile ranges, using L‐statistics
提出高精度非参数方法，用于无条件或条件下两个总体分位数差异的推断，对应分位数处理效应，通过概率积分变换和狄利克雷分布选取L统计量构建置信区间，模拟显示稳健且长度更短。
We provide novel, high‐order accurate methods for non‐parametric inference on quantile differences between two populations in both unconditional and conditional settings. These quantile differences correspond to (conditional) quantile treatment effects under (conditional) independence of a binary treatment and potential outcomes. Our methods use the probability integral transform and a Dirichlet (rather than Gaussian) reference distribution to pick appropriate L‐statistics as confidence interval endpoints, achieving high‐order accuracy. Using a similar approach, we also propose confidence intervals/sets for vectors of quantiles, interquantile ranges and differences of linear combinations of quantiles. In the conditional setting, when smoothing over continuous covariates, optimal bandwidth and coverage probability rates are derived for all methods. Simulations show that the new confidence intervals have a favourable combination of robust accuracy and short length compared with existing approaches. Detailed steps for confidence interval construction are provided in online Appendix E as supporting information, and code for all methods, simulations and empirical examples is provided.