Model-based bootstrap for detection of regional quantile treatment effects

Quantile treatment effects are often considered in a quantile regression framework to adjust for the effect of covariates. In this study, we focus on the problem of testing whether the treatment effect is significant at a set of quantile levels (e.g. lower quantiles). We propose a regional quantile regression rank test as a generalisation of the rank test at an individual quantile level. This test statistic allows us to detect the treatment effect for a prespecified quantile interval by integrating the regression rank scores over the region of interest. A new model-based bootstrap method is constructed to estimate the null distribution of the test statistic. A simulation study is conducted to demonstrate the validity and usefulness of the proposed test. We also demonstrate the use of the proposed method through an analysis of the 2016 US birth weight data and selected S&P 500 sector portfolio data.