COMBINED PENALIZED QUANTILE REGRESSION IN HIGH DIMENSIONAL MODELS
COMBINED PENALIZED QUANTILE REGRESSION IN HIGH DIMENSIONAL MODELS
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发表时间：
2015
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通讯作者：
Muhammad Amin;Lixin Song;Milton Abdul Thorlie;Xiaoguang Wang
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作者：
Muhammad Amin;Lixin Song;Milton Abdul Thorlie;Xiaoguang Wang
分位数回归技术被认为是一种替代经典的普通最小二乘（OLS）回归的情况下存在的离群值和重尾误差的线性模型。本文建立了参数个数为发散的稀疏分位数回归的相合性、渐近正态性和预言性。并给出了组合惩罚估计的收敛速度。并将秩相关筛选方法应用于一维数据的处理。仿真研究，分析的享乐住宅价格和清洁空气的需求数据集进行说明所提出的方法的有限样本性能。
The quantile regression technique is considered as an alternative to the classical ordinary least squares (OLS) regression in case of outliers and heavy tailed errors existing in linear models. In this work, the consistency, asymptotic normality, and oracle property are established for sparse quantile regression with a diverging number of parameters. The rate of convergence of the combined penalized estimator is also established. Furthermore, the rank correlation screening (RCS) method is applied to deal with an ultrahigh dimensional data. The simulation studies, the analysis of hedonic housing prices and the demand for clean air dataset are conducted to illustrate the finite sample performance of the proposed method.