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### 基于外推中间次序分位数的极端条件分位数估计

1. 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.

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

1. 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

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.

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