Estimation of high conditional quantiles using the Hill estimator of the tail index

Fengyang He, Yebin Cheng*, Tiejun TONG

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)


To implement the extremal quantile regression, one needs to have an accurate estimate of the tail index that is involved in the limit distributions of extremal regression quantiles. However, the existing quantile estimation methods are often unstable owing to data sparsity in the tails. In this paper, we propose the Hill estimator for the tail index based on regression quantiles, and construct a new estimator for high conditional quantiles through an extrapolation of the intermediate regression quantiles. In both theory and simulation, we demonstrate that the proposed estimators are more efficient than those based on the refined Pickands estimator of the tail index. The applicability of the new method is also illustrated on the Occidental Petroleum daily stock return data.

Original languageEnglish
Pages (from-to)64-77
Number of pages14
JournalJournal of Statistical Planning and Inference
Publication statusPublished - 1 Sept 2016

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Extreme value theory
  • High conditional quantiles
  • Hill estimator
  • Pickands estimator
  • Quantile regression
  • Tail index


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