Robust spline-based variable selection in varying coefficient model
Robust spline-based variable selection in varying coefficient model
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DOI：
10.1007/s00184-014-0491-y
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发表时间：
2015
期刊：
影响因子：
0.7
通讯作者：
Long Feng;Changliang Zou;Zhaojun Wang;Xianwu Wei;Bin Chen
中科院分区：
文献类型：
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作者：
Long Feng;Changliang Zou;Zhaojun Wang;Xianwu Wei;Bin Chen
变系数模型是线性回归模型的一种推广，应用广泛。许多程序已经开发的模型估计，最近有效的变量选择程序的变系数模型已经提出。然而，这些变量选择方法主要建立在最小二乘（LS）类型的方法上。虽然LS方法在变系数模型拟合和变量选择中是成功的和标准的选择，但当误差遵循重尾分布或存在离群值时，它可能会受到影响。为了克服这个问题，我们首先开发了一种新的鲁棒估计，称为基于秩的样条估计，它结合了秩推断和多项式样条的思想。此外，我们提出了一个强大的变量选择方法，将平滑剪切绝对偏差惩罚到基于秩的样条损失函数。在温和的条件下，我们从理论上证明了所提出的基于秩的样条估计是非常有效的广泛的分布。它的渐近相对效率相对于LS为基础的方法是密切相关的符号秩Wilcoxon检验相对于thetest。此外，所提出的变量选择方法可以一致地识别真实模型，并且所得到的估计量可以与Oracle估计量一样有效。仿真研究表明，当误差偏离正态分布时，该方法比基于LS的方法具有更好的性能。
The varying coefficient model is widely used as an extension of the linear regression model. Many procedures have been developed for the model estimation, and recently efficient variable selection procedures for the varying coefficient model have been proposed as well. However, those variable selection approaches are mainly built on the least-squares (LS) type method. Although the LS method is a successful and standard choice in the varying coefficient model fitting and variable selection, it may suffer when the errors follow a heavy-tailed distribution or in the presence of outliers. To overcome this issue, we start by developing a novel robust estimator, termed rank-based spline estimator, which combines the ideas of rank inference and polynomial spline. Furthermore, we propose a robust variable selection method, incorporating the smoothly clipped absolute deviation penalty into the rank-based spline loss function. Under mild conditions, we theoretically show that the proposed rank-based spline estimator is highly efficient across a wide spectrum of distributions. Its asymptotic relative efficiency with respect to the LS-based method is closely related to that of the signed-rank Wilcoxon test with respect to thettest. Moreover, the proposed variable selection method can identify the true model consistently, and the resulting estimator can be as efficient as the oracle estimator. Simulation studies show that our procedure has better performance than the LS-based method when the errors deviate from normality.