Closed-based testing when multiple quantile regressions are fitted

This paper addresses the challenge of conducting multiple quantile regressions at different levels and the consequent issue of controlling the familywise error rate (FWER). Current practices in various fields typically involve conducting separate tests for each quantile, leading to a multiplicity problem that often remains unaddressed. We propose a method that integrates the Wald test within a closed-testing procedure to manage multiple tests effectively. We conduct simulation studies across various scenarios to demonstrate the efficacy of our method in control-ling the FWER and its power compared to traditional approaches like the Bonferroni correction. Our findings advocate for a more rigorous application of statistical tests in quantile regressions to prevent false discoveries and enhance the reliability of analytical conclusions.