Varying covariate effects often manifest meaningful heterogeneity in covariate-response associations. In this paper, we adopt a quantile regression model that assumes linearity at a continuous range of quantile levels as a tool to explore such data dynamics. The consideration of potential non-constancy of covariate effects necessitates a new perspective for variable selection, which, under the assumed quantile regression model, is to retain variables that have effects on all quantiles of interest as well as those that influence only part of quantiles considered. Current work on l ₁-penalized quantile regression either does not concern varying covariate effects or may not produce consistent variable selection in the presence of covariates with partial effects, a practical scenario of interest. In this work, we propose a shrinkage approach by adopting a novel uniform adaptive LASSO penalty. The new approach enjoys easy implementation without requiring smoothing. Moreover, it can consistently identify the true model (uniformly across quantiles) and achieve the oracle estimation efficiency. We further extend the proposed shrinkage method to the case where responses are subject to random right censoring. Numerical studies confirm the theoretical results and support the utility of our proposals.

中文翻译：

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基于分位数回归的不同协变量效应的收缩估计。

不同的协变量效应通常在协变量-响应关联中表现出有意义的异质性。在本文中，我们采用分位数回归模型，该模型假设分位数水平的连续范围内呈线性，作为探索此类数据动态的工具。考虑协变量效应的潜在非恒定性需要一个新的变量选择视角，在假定的分位数回归模型下，保留对所有感兴趣的分位数有影响的变量以及仅影响部分分位数的变量. 目前在l _{1 上的}工作- 惩罚分位数回归要么不涉及变化的协变量效应，要么在存在具有部分效应的协变量的情况下可能无法产生一致的变量选择，这是一个有趣的实际场景。在这项工作中，我们通过采用新颖的统一自适应 LASSO 惩罚提出了一种收缩方法。新方法无需平滑即可轻松实施。此外，它可以一致地识别真实模型（均匀跨分位数）并实现预言机估计效率。我们进一步将建议的收缩方法扩展到响应受到随机右删失的情况。数值研究证实了理论结果并支持我们建议的实用性。