Scale calibration for high-dimensional robust regression
Scale calibration for high-dimensional robust regression
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DOI：
10.1214/21-ejs1936
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发表时间：
2018-11
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通讯作者：
Po-Ling Loh
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文献类型：
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作者：
Po-Ling Loh
当加性误差的尺度参数未知时，我们提出了一种新的高维线性回归方法。所提出的估计是基于惩罚的Huber$M$-估计，其估计误差的理论结果最近在高维统计文献中被提出。然而，线性模型中误差项的方差与用于定义Huber损失形状的最优参数复杂地联系在一起。我们的主要思想是使用基于Lepski方法的自适应技术来克服关于位置和尺度参数的联合非凸优化问题的困难。
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error have recently been proposed in high-dimensional statistics literature. However, the variance of the error term in the linear model is intricately connected to the optimal parameter used to define the shape of the Huber loss. Our main idea is to use an adaptive technique, based on Lepski's method, to overcome the difficulties in solving a joint nonconvex optimization problem with respect to the location and scale parameters.