Xu Jinfeng, Ying Zhiliang
Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546, Singapore.
Ann Inst Stat Math. 2010 Jun 1;62(3):487-514. doi: 10.1007/s10463-008-0184-2.
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.
我们考虑用于变量选择的带有LASSO型惩罚项的中位数回归。在回归模型中变量数量固定的情况下，提出了一种两阶段方法用于同时估计和变量选择，其中惩罚程度是自适应选择的。提出并使用了一种贝叶斯信息准则类型的方法来获得一个数据驱动的程序，该程序被证明能自动选择渐近最优的调优参数。结果表明，所得估计量具有所谓的神谕性质。中位数回归和LASSO惩罚的结合通过标准线性规划在计算上易于实现。可以利用随机扰动方案来获得标准误差的简单估计量。进行了模拟研究以评估所提方法的有限样本性能。我们用一个实际例子来说明该方法。
