标题： 全局自适应分位数回归与超高维数据 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在实践中经常遇到的异质协变量-响应关联的有用工具。 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分位数水平上的模型稀疏性检查，这些水平通常由用户随意指定。 由此得到的模型可能对分位数水平的具体选择敏感，导致解释困难并削弱对结果的信心。 在本文中，我们提出了一个用于高维情况下分位数回归的新惩罚框架。 我们采用自适应L1惩罚，并且更重要的是，为一组分位数水平提出了一种统一的调参选择方法，以避免在单个分位数水平上模型选择的一些潜在问题。 我们提出的方法在连续的分位数水平范围内实现了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稳健性。 我们的理论结果包括统一收敛的oracle速率和参数估计量的弱收敛性。 我们还使用数值研究来确认我们的理论结果，并说明我们提议的实用性。 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