Can’t Ridge Regression Perform Variable Selection?
Can’t Ridge Regression Perform Variable Selection?
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DOI：
10.1080/00401706.2020.1791254
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发表时间：
2020-07
期刊：
影响因子：
2.5
通讯作者：
Yichao Wu
中科院分区：
文献类型：
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作者：
Yichao Wu
摘要为了解决普通最小二乘估计由于多重共线性引起的不稳定性问题，引入岭回归。它本质上是通过对回归系数施加脊惩罚来惩罚最小二乘损失。脊罚将回归系数估计缩小到零，但不完全为零。由于这个原因，岭回归长期以来一直被批评不能进行变量选择。在本文中，我们提出了一种新的基于单独惩罚岭回归的变量选择方法，这是岭回归的一个稍微广义的版本。还提供了自适应版本。通过仿真和实际数据算例表明，本文提出的方法具有较好的性能。
Abstract Ridge regression was introduced to deal with the instability issue of the ordinary least squares estimate due to multicollinearity. It essentially penalizes the least squares loss by applying a ridge penalty on the regression coefficients. The ridge penalty shrinks the regression coefficient estimate toward zero, but not exactly zero. For this reason, the ridge regression has long been criticized of not being able to perform variable selection. In this article, we proposed a new variable selection method based on an individually penalized ridge regression, a slightly generalized version of the ridge regression. An adaptive version is also provided. Our new methods are shown to perform competitively based on simulation and a real data example.