Zhu Hanbing, Zhang Riquan, Li Yehua, Yao Weixin
East China Normal University.
University of California, Riverside.
Stat Sin. 2022 Oct;32(4):1767-1787.
Quantile regression as an alternative to modeling the conditional mean function provides a comprehensive picture of the relationship between a response and covariates. It is particularly attractive in applications focused on the upper or lower conditional quantiles of the response. However, conventional quantile regression estimators are often unstable at the extreme tails, owing to data sparsity, especially for heavy-tailed distributions. Assuming that the functional predictor has a linear effect on the upper quantiles of the response, we develop a novel estimator for extreme conditional quantiles using a functional composite quantile regression based on a functional principal component analysis and an extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator under some regularity conditions, and compare it with other estimation methods using Monte Carlo simulations. Finally, we demonstrate the proposed method by empirically analyzing two real data sets.
分位数回归作为一种替代条件均值函数建模的方法，提供了响应变量与协变量之间关系的全面图景。在关注响应变量的上条件分位数或下条件分位数的应用中，它特别具有吸引力。然而，由于数据稀疏性，传统的分位数回归估计量在极端尾部通常不稳定，特别是对于重尾分布。假设函数型预测变量对响应变量的上分位数有线性影响，我们基于函数主成分分析和极值理论的外推技术，开发了一种使用函数复合分位数回归的极端条件分位数的新型估计量。在一些正则条件下，我们建立了所提出估计量的渐近正态性，并通过蒙特卡罗模拟将其与其他估计方法进行比较。最后，我们通过对两个真实数据集进行实证分析来展示所提出的方法。
