Simultaneous confidence bands for extremal quantile regression with splines
Simultaneous confidence bands for extremal quantile regression with splines
复制标题
DOI：
10.1007/s10687-019-00360-4
复制
发表时间：
2019-08
期刊：
影响因子：
1.3
通讯作者：
Takuma Yoshida
中科院分区：
文献类型：
--
作者：
Takuma Yoshida
本研究利用样条法研究了极值分位数回归的同时置信带。利用传统的分位数回归框架构造了中阶分位数的样条估计量，并通过外推中阶分位数的样条估计量得到了极阶分位数估计量。我们建立了中阶和极阶分位数的样条和外推估计的渐近正态性。将管体积公式应用于上述两个估计量，构造了中阶和极阶分位数的同时条件分位数置信带。为了验证所提出的置信区间的性能，我们使用蒙特卡罗模拟和一个具有真实数据的示例。
This study investigates simultaneous confidence bands for extremal quantile regressions using the spline method. We construct the spline estimator for intermediate order quantiles using a conventional quantile regression framework, and we obtain the extreme order quantile estimator by extrapolating the spline estimator for intermediate order quantiles. We establish the asymptotic normality of the spline and extrapolated estimators for intermediate and extreme order quantiles. By applying the volume of tube formula to the above two estimators, we construct simultaneous conditional quantile confidence bands for intermediate and extreme order quantiles. To confirm the performance of the proposed confidence bands, we use a Monte Carlo simulation and an example with real data.