论文标题
高维异质的平均回归中的支持估计
Support estimation in high-dimensional heteroscedastic mean regression
论文作者
论文摘要
当前的高维统计研究研究涉及与普遍的轻尾假设的偏差有关的可用方法。在本文中，我们考虑了一个线性平均回归模型，该模型具有随机设计和潜在的异质，重尾误差，并研究了该框架中的支持估计。我们使用严格的凸，平滑的Huber损耗函数变体，并根据问题的参数以及计算效率的自适应套索惩罚，并根据调整参数进行调整参数。对于由此产生的估计器，我们显示出$ \ ell_ \ infty $ norm中的标志一致性和最佳收敛速率，如在同型，轻尾设置中。在我们的分析中，我们必须处理以下问题：即使对于Huber损耗函数的调谐参数的小值，线性均值回归模型中目标参数的支持及其可靠版本也可能有所不同。模拟说明了所提出的方法的有利数值性能。
A current strand of research in high-dimensional statistics deals with robustifying the available methodology with respect to deviations from the pervasive light-tail assumptions. In this paper we consider a linear mean regression model with random design and potentially heteroscedastic, heavy-tailed errors, and investigate support estimation in this framework. We use a strictly convex, smooth variant of the Huber loss function with tuning parameter depending on the parameters of the problem, as well as the adaptive LASSO penalty for computational efficiency. For the resulting estimator we show sign-consistency and optimal rates of convergence in the $\ell_\infty$ norm as in the homoscedastic, light-tailed setting. In our analysis, we have to deal with the issue that the support of the target parameter in the linear mean regression model and its robustified version may differ substantially even for small values of the tuning parameter of the Huber loss function. Simulations illustrate the favorable numerical performance of the proposed methodology.
