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Robust variable selection of varying coefficient partially nonlinear model based on quantile regression

机译：基于量子回归的变系数部分非线性模型的鲁棒变量选择

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摘要

Quantile regression has been a popular topic for robust inference in semi-parametric models. However, there does not exist related literature for the varying coefficient partially nonlinear model (VCPNLM), which is the focus of this paper. Let alone on the quantile variable selection of VCPNLM. Specifically, via iteratively minimizing an average check loss estimation procedure based on quantile loss function, we propose a profile-type nonlinear quantile regression method for the VCPNLM, and further establish the asymptotic properties of the resulting estimators under some mild regularity conditions. In addition, to achieve sparsity when there exist irrelevant variables, we develop a variable selection procedure for high-dimensional VCPNLM by using the idea of shrinkage, and then demonstrate its oracle property. Two most important parameters including the smoothing parameter and the tuning parameter are also discussed, respectively. Finally, extensive numerical simulations with various errors are conducted to evaluate the finite sample performance of estimation and variable selection, and a real data analysis is further presented to illustrate the application of the proposed methods.
机译：Smastile回归是半参数模型中强大推理的流行主题。然而，不存在于不同系数部分非线性模型（VCPNLM）的相关文献，这是本文的焦点。更不用说VCPNLM的定量变量选择。具体地，通过迭代地最小化基于定量损失函数的平均校验损耗估计过程，我们提出了一种用于VCPNLM的轮廓型非线性分量回归方法，并进一步在一些轻度规则性条件下建立所得估计器的渐近性质。此外，在存在不相关的变量时实现稀疏性，我们使用缩收的思想开发了高维VCPNLM的变量选择过程，然后演示其Oracle属性。还分别讨论了包括平滑参数和调谐参数的两个最重要的参数。最后，进行了具有各种误差的广泛数值模拟，以评估估计和可变选择的有限样本性能，并且还进一步提出了实际数据分析以说明所提出的方法的应用。

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