Abstract

The estimation of conditional quantiles at extreme tails is of great inter

est in numerous applications. Various methods that integrate regression analysis

with an extrapolation strategy derived from extreme value theory have been proposed to estimate extreme conditional quantiles in scenarios with a fixed number

of covariates. However, these methods become less effective in high-dimensional

settings, where the number of covariates grows with the sample size. In this article, we develop new estimation methods tailored for extreme conditional quantiles

with high-dimensional covariates. We establish the asymptotic properties of the

proposed estimators and demonstrate their superior performance through simulation studies, particularly in scenarios of growing dimension and high dimension

where existing methods may fail. Furthermore, the analysis of auto insurance

data validates the efficacy of our methods in estimating extreme conditional

insurance claims and selecting important variables.

Key words and phrases: Extrapolation; Extreme value; High-dimensional data; Regression analysis

Information

Preprint No.SS-2025-0044
Manuscript IDSS-2025-0044
Complete AuthorsYiwei Tang, Huixia Judy Wang, Deyuan Li
Corresponding AuthorsDeyuan Li
Emailsdeyuanli@fudan.edu.cn

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Acknowledgments

Deyuan Li’s research was partially supported by the National Natural Science Foundation of China grants 11971115 and 12471279.

Supplementary Materials

The supplementary materials comprise a PDF titled Supplementary Material for High-dimensional Extreme Quantile Regression—containing techni-

cal conditions, proofs, simulation results, and extra details on the auto insurance claims data—and a CSV file with the auto insurance claims dataset

used in Section 4.

Supplementary materials are available for download.