Multiplier bootstrap tests for high-dimensional quantile regression

When dealing with skewed and asymmetric data, quantile regression is an important analytical tool due to its robustness. This paper investigates the test procedure for the significance of regression coefficients in high-dimensional quantile regression. We first investigate the asymptotic properties of score-based test statistics and find that their limiting null distribution depends on the eigenstructure of the covariance matrices, leaving the practitioner in a bind. Since checking covariance structures in the context of high-dimensional data is challenging, we propose a multiplier bootstrap test procedure for practical implementation. We also establish the validity of the testing procedure under both the null and alternative hypotheses. The results of our numerical studies on both simulated and real data demonstrate that the proposed test procedure shows highly promising performance across a diverse range of scenarios.