基于外推中间次序分位数的极端条件分位数估计

doi:10.12341/jssms21129

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (2): 434-461.DOI: 10.12341/jssms21129

基于外推中间次序分位数的极端条件分位数估计

杨晓蓉, 李路, 吴士迪, 徐诗展

浙江工商大学统计与数学学院, 杭州 310018;浙江工商大学统计数据工程技术与应用协同创新中心, 杭州 310018

收稿日期:2021-03-15 修回日期:2021-09-28 出版日期:2022-02-25 发布日期:2022-03-21
通讯作者: 杨晓蓉,Email:xryang@zjgsu.edu.cn.
基金资助:
浙江省自然科学基金（LY22A010006），国家社会科学基金（17BTJ027），浙江省重点建设高校优势特色学科（浙江工商大学），浙江工商大学统计数据工程技术与应用协同创新中心，浙江省属高校基本业务专项基金资助课题.

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杨晓蓉, 李路, 吴士迪, 徐诗展. 基于外推中间次序分位数的极端条件分位数估计[J]. 系统科学与数学, 2022, 42(2): 434-461.

YANG Xiaorong, LI Lu, WU Shidi, XU Shizhan. Extreme Conditional Quantile Estimation via Extrapolated Intermediate Ordinal Quantiles[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(2): 434-461.

Extreme Conditional Quantile Estimation via Extrapolated Intermediate Ordinal Quantiles

YANG Xiaorong, LI Lu, WU Shidi, XU Shizhan

School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018;Collaborative Innovation Center of Statistical Data Engineering Technology and Application, Zhejiang Gongshang University, Hangzhou 310018

Received:2021-03-15 Revised:2021-09-28 Online:2022-02-25 Published:2022-03-21

近年来，条件分位数估计被广泛应用于金融、生物和医学等众多领域.在研究协变量对响应变量在不同分位数水平的影响时，分位数回归方法是一种贴切且有效的估计方法.然而，由于尾部数据的稀疏性，用分位数回归来估计极端条件分位数通常会产生较大的估计误差.文章将极值理论与分位数回归结合起来，利用中间条件分位数外推法，研究线性分位数回归模型尾部极端分位数水平的估计.基于核函数修正了现有方法中对极值指数和极端条件分位数估计的渐近有偏性，得到了一种渐近无偏的尾部估计量，并论证了其渐近正态性.数值模拟和实例数据分析表明，文章所提方法具有一定的稳定性，即中间分位数个数的不同取值对极值指数和极端条件分位数的估计不会产生较大的影响.

关键词： 极值理论, 极值指数, 极端条件分位数, 中间次序分位数

In recent years, conditional quantile estimation regression has been widely used in finance, biology, and medicine. Quantile regression is an appropriate and effective method to estimate the influences of covariates on the responses at different quantile levels. However, due to the sparsity of the tail data, there is usually a large bias when the quantile regression method is used to estimate extreme conditional quantiles. In this paper, the extreme value theory and the quantile regression are combined to estimate the extreme quantile levels at the tail of the linear quantile regression model with an extrapolation of intermediate conditional quantiles. Based on the kernel function, the bias-corrected tail estimators are constructed, and their asymptotic normality is proved. Both numerical simulation and the real data analysis both show that the proposed method has a certain stability, that is, the number of intermediate quantiles has no large impacts on the estimation of extreme value index and extreme condition quantiles.

Key words: Extreme value theory, extreme value index, extreme conditional quantile, intermediate ordinal quantile

MR(2010)主题分类:

62G86
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