  Quantile regression has become a valuable tool to analyze heterogeneous
covaraite-response associations that are often encountered in practice. The
development of quantile regression methodology for high-dimensional covariates
primarily focuses on examination of model sparsity at a single or multiple
quantile levels, which are typically pre-specified ad hoc by the users. The
resulting models may be sensitive to the specific choices of the quantile
levels, leading to difficulties in interpretation and erosion of confidence in
the results. In this article, we propose a new penalization framework for
quantile regression in the high-dimensional setting. We employ adaptive L1
penalties, and more importantly, propose a uniform selector of the tuning
parameter for a set of quantile levels to avoid some of the potential problems
with model selection at individual quantile levels. Our proposed approach
achieves consistent shrinkage of regression quantile estimates across a
continuous range of quantiles levels, enhancing the flexibility and robustness
of the existing penalized quantile regression methods. Our theoretical results
include the oracle rate of uniform convergence and weak convergence of the
parameter estimators. We also use numerical studies to confirm our theoretical
findings and illustrate the practical utility of our proposal
