Quantile-Regression Inference With Adaptive Control of Size

Regression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors. This article develops a new estimate of the asymptotic variance of regression quantiles that leads any resulting Wald-type test or confidence region to behave as well in large samples as its infeasible counterpart in which the true conditional response densities are embedded. We give explicit guidance on implementing the new variance estimator to control adaptively the size of any resulting Wald-type test. Monte Carlo evidence indicates the potential of our approach to deliver powerful tests of heterogeneity of quantile treatment effects in covariates with good size performance over different quantile levels, data-generating processes, and sample sizes. We also include an empirical example. Supplementary material is available online.回归分位数（regression quantiles）的渐近方差，取决于给定回归元时响应变量的条件密度。本文提出了一种全新的回归分位数渐近方差估计方法，使得由此构造的瓦尔德型检验（Wald-type test）或置信区域，在大样本下的表现与嵌入真实条件响应密度的不可行基准版本完全一致。针对该新型方差估计量的实际实现，本文给出了明确操作指引，用以自适应控制所得瓦尔德型检验的显著性水平。蒙特卡洛（Monte Carlo）模拟结果表明，本文所提方法可用于构建针对协变量中分位数处理效应（quantile treatment effects）异质性的高检验效能检验，且在不同分位数水平、数据生成过程（data-generating processes）与样本量下均能保持优异的显著性水平控制效果。本文同时附带一则实证案例。补充材料可在线获取。