This paper tackles the challenge of performing multiple quantile regressions across different quantile levels and the associated problem of controlling the familywise error rate, an issue that is generally overlooked in practice. We propose a multivariate extension of the rank-score test and embed it within a closed-testing procedure to efficiently account for multiple testing. Then we further generalize the multivariate test to enhance statistical power against alternatives in selected directions. Theoretical foundations and simulation studies demonstrate that our method effectively controls the familywise error rate while achieving higher power than traditional corrections, such as Bonferroni.

翻译：本文解决了在不同分位数水平上执行多重分位数回归的挑战，以及与之相关的族系错误率控制问题——这一问题在实践中常被忽视。我们提出了秩评分检验的多元扩展，并将其嵌入封闭检验程序，以有效处理多重检验。随后，我们进一步推广了多元检验，以在选定的方向上增强备择假设下的统计功效。理论基础和模拟研究表明，我们的方法在有效控制族系错误率的同时，比邦费罗尼等传统校正方法具有更高的功效。