Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions

Jianqing Fan Quefeng Li Yuyan Wang

Statistics Theory and Methods mathscidoc:1912.43318

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79, (1), 247-265, 2017.1
Data subject to heavytailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and least absolute deviation regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in ultrahigh dimensional settings with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss. Such a penalized robust approximate (RA) quadratic loss will be called the RA lasso. In the ultrahigh dimensional setting, where the dimensionality can grow exponentially with the sample size
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@inproceedings{jianqing2017estimation,
  title={Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions},
  author={Jianqing Fan, Quefeng Li, and Yuyan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113700651104878},
  booktitle={Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
  volume={79},
  number={1},
  pages={247-265},
  year={2017},
}
Jianqing Fan, Quefeng Li, and Yuyan Wang. Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions. 2017. Vol. 79. In Journal of the Royal Statistical Society: Series B (Statistical Methodology). pp.247-265. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113700651104878.
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