We consider the median regression with a LASSO-type penalty term for variable selection. With the fixed number of variables in regression model, a two-stage method is proposed for simultaneous estimation and variable selection where the degree of penalty is adaptively chosen. A Bayesian information criterion type approach is proposed and used to obtain a data-driven procedure which is proved to automatically select asymptotically optimal tuning parameters. It is shown that the resultant estimator achieves the so-called oracle property. The combination of the median regression and LASSO penalty is computationally easy to implement via the standard linear programming. A random perturbation scheme can be made use of to get simple estimator of the standard error. Simulation studies are conducted to assess the finite-sample performance of the proposed method. We illustrate the methodology with a real example.

中文翻译：

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使用套索型惩罚的中值回归中的同时估计和变量选择

我们考虑使用 LASSO 类型惩罚项进行变量选择的中值回归。在回归模型中变量数量固定的情况下，提出了一种自适应选择惩罚程度的同时估计和变量选择的两阶段方法。提出了一种贝叶斯信息准则类型的方法，并用于获得一个数据驱动的程序，该程序被证明可以自动选择渐近最优的调整参数。结果表明，结果估计器实现了所谓的预言机属性。通过标准线性规划，中值回归和 LASSO 惩罚的组合在计算上很容易实现。可以使用随机扰动方案来获得标准误差的简单估计量。进行模拟研究以评估所提出方法的有限样本性能。我们用一个真实的例子来说明这个方法。