Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate

作     者：Feng Yang HE Ye Bin CHENG Tie Jun TONG 

作者机构：Department of Statistics Ji'nan University Guangzhou 510632 P. R. China Glorious Sun School of Business and Management Donghua University Shanghai 250001 P. R. China Department of Mathematics Hong Kong Baptist University Hong Kong P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第10期

页      面：1589-1610页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11671338) the Hong Kong Baptist University(Grant Nos.FRG1/16-17/018 and FRG2/16-17/074) 

主　　题：Extreme conditional quantile extreme value theory nonparametric modeling functional covariate 

摘      要：Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.