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：本文针对在不同分位数水平上执行多重分位数回归的挑战，以及控制族错误率这一实践中常被忽视的相关问题展开研究。我们提出了秩得分检验的多元扩展，并将其嵌入封闭检验程序中，以有效处理多重检验问题。随后，我们进一步推广该多元检验方法，以增强对特定方向备择假设的统计功效。理论分析与模拟研究表明，所提方法在实现比传统校正方法（如Bonferroni校正）更高统计功效的同时，能有效控制族错误率。