Wild residual bootstrap inference for penalized quantile regression with heteroscedastic errors
Wild residual bootstrap inference for penalized quantile regression with heteroscedastic errors
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DOI：
10.1093/biomet/asy037
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发表时间：
2018-07
期刊：
影响因子：
2.7
通讯作者：
Lan Wang;I. Van Keilegom;Adam Maidman
中科院分区：
文献类型：
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作者：
Lan Wang;I. Van Keilegom;Adam Maidman
摘要我们考虑了一个异方差回归模型，其中一些回归系数为零，但不知道哪些为零。惩罚分位数回归是分析此类数据的一种有用的方法。通过允许不同的协变量与不同分位数水平上的条件分位数函数的建模相关，它提供了比均值回归更完整的响应变量的条件分布的图景。现有的关于惩罚分位数回归的工作主要集中在点估计上。虽然Bootstrap方法最近被证明对惩罚均值回归的推断是有效的，但它们不能直接适用于具有异方差误差的惩罚分位数回归。我们证明了非惩罚分位数回归的野生剩余Bootstrap过程对于逼近具有自适应L1惩罚的惩罚分位数回归估计的分布是渐近有效的，并且改进的形式可以用来逼近L1惩罚分位数回归估计的分布。新方法不需要估计未知的误差密度函数。我们建立了一致性，证明了有限样本的性能，并在一个真实的数据例子上说明了应用。
Summary We consider a heteroscedastic regression model in which some of the regression coefficients are zero but it is not known which ones. Penalized quantile regression is a useful approach for analysing such data. By allowing different covariates to be relevant for modelling conditional quantile functions at different quantile levels, it provides a more complete picture of the conditional distribution of a response variable than mean regression. Existing work on penalized quantile regression has been mostly focused on point estimation. Although bootstrap procedures have recently been shown to be effective for inference for penalized mean regression, they are not directly applicable to penalized quantile regression with heteroscedastic errors. We prove that a wild residual bootstrap procedure for unpenalized quantile regression is asymptotically valid for approximating the distribution of a penalized quantile regression estimator with an adaptive L1 penalty and that a modified version can be used to approximate the distribution of a L1‐penalized quantile regression estimator. The new methods do not require estimation of the unknown error density function. We establish consistency, demonstrate finite‐sample performance, and illustrate the applications on a real data example.