论文标题
通过多个损失功能和选票选择的惩罚回归
Penalized regression with multiple loss functions and selection by vote
论文作者
论文摘要
本文在高维数据方案中考虑了线性模型。我们提出了一个使用多个损失函数来选择相关预测因子和估计参数并研究其渐近特性的过程。可变选择是通过称为“投票”的程序进行的，该程序汇总了受损失功能的结果。使用多个目标函数分别简化算法并允许并行计算，这是方便且快速的。作为一个特殊的例子，我们考虑了一个分位数回归模型，该模型可最佳地结合多个分位水平。我们表明，参数矢量的结果估计器在渐近上是有效的。模拟和数据应用程序确认了我们方法的三个主要优点：（a）降低可变选择的错误发现率； （b）提高参数估计的质量； （c）提高计算效率。
This article considers a linear model in a high dimensional data scenario. We propose a process which uses multiple loss functions both to select relevant predictors and to estimate parameters, and study its asymptotic properties. Variable selection is conducted by a procedure called "vote", which aggregates results from penalized loss functions. Using multiple objective functions separately simplifies algorithms and allows parallel computing, which is convenient and fast. As a special example we consider a quantile regression model, which optimally combines multiple quantile levels. We show that the resulting estimators for the parameter vector are asymptotically efficient. Simulations and a data application confirm the three main advantages of our approach: (a) reducing the false discovery rate of variable selection; (b) improving the quality of parameter estimation; (c) increasing the efficiency of computation.
