标题： 具有超高维数据的全局自适应分位数回归 显示英文标题

标题： Globally adaptive quantile regression with ultra-high dimensional data

摘要： 分位数回归已成为分析实践中经常遇到的异质协变量-反应关联的重要工具。 对于高维协变量的分位数回归方法的发展主要集中在单个或多个预设的分位数水平上模型稀疏性的检验，这些分位数水平通常是用户随意指定的。 由此产生的模型可能对分位数水平的具体选择敏感，导致解释困难以及对结果信心的削弱。 本文中，我们提出了一个适用于高维情况下的新的分位数回归惩罚框架。 我们采用了自适应L1惩罚，并且更重要的是，提出了一组分位数水平的统一调参选择方法，以避免在个体分位数水平上的模型选择可能带来的某些潜在问题。 我们所提出的这种方法能够在连续的分位数水平范围内实现回归分位数估计的一致收缩，增强了现有惩罚分位数回归方法的灵活性和鲁棒性。 我们的理论结果包括参数估计的oracle收敛速度和弱收敛性。 我们也通过数值研究验证了我们的理论发现，并展示了我们所提出方法的实际效用。 显示英文摘要

摘要： 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