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Acta Mathematica Sinica, English Series

, Volume 34, Issue 10, pp 1589–1610 | Cite as

Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate

  • Feng Yang He
  • Ye Bin Cheng
  • Tie Jun Tong
Article

Abstract

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.

Keywords

Extreme conditional quantile extreme value theory nonparametric modeling functional covariate 

MR(2010) Subject Classification

62G32 

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Notes

Acknowledgements

The authors thank the editor, the associate editor and two referees for their constructive comments that have led to a substantial improvement of the paper.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsJi’nan UniversityGuangzhouP. R. China
  2. 2.Glorious Sun School of Business and ManagementDonghua UniversityShanghaiP. R. China
  3. 3.Department of MathematicsHong Kong Baptist UniversityHong KongP. R. China

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