Extremal linear quantile regression with weibull-type tails

Type
Article

Authors
He, Fengyang
Wang, Huixia Judy
Tong, Tiejun

KAUST Grant Number
OSR-2015-CRG4-2582

Date
2020

Abstract
This study examines the estimation of extreme conditional quantiles for distributions with Weibull-type tails. We propose two families of estimators for the Weibull tail-coefficient, and construct an extrapolation estimator for the extreme conditional quantiles based on a quantile regression and extreme value theory. The asymptotic results of the proposed estimators are established. This work fills a gap in the literature on extreme quantile regressions, where many important Weibull-type distributions are excluded by the assumed strong conditions. A simulation study shows that the proposed extrapolation method provides estimations of the conditional quantiles of extreme orders that are more efficient and stable than those of the conventional method. The practical value of the proposed method is demonstrated through an analysis of extremely high birth weights.

Citation
He, F., Wang, H. J., & Tong, T. (2020). Extremal linear quantile regression with Weibull-type tails. Statistica Sinica. doi:10.5705/ss.202018.0073

Acknowledgements
This research was partly supported by the National Natural Science Foundation of China grants No.11671338 and No.11690012, the National Science Foundation (NSF) grant DMS-1712760, the IR/D program from the NSF, the Hunan Province education scientific research project grant No. 19C1054, and the OSR-2015-CRG4-2582 grant from KAUST. The authors thank the editor, the associate editor, and two referees for their constructive comments.

Publisher
Statistica Sinica (Institute of Statistical Science)

Journal
Statistica Sinica

DOI
10.5705/ss.202018.0073

Additional Links
http://www3.stat.sinica.edu.tw/statistica/J30N3/J30N310/J30N310.html

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