Estimation of extreme depth-based quantile regions

Yi He, John Einmahl

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)


Consider the extreme quantile region induced by the half‐space depth function HD of the form , such that  for a given, very small p>0. Since this involves extrapolation outside the data cloud, this region can hardly be estimated through a fully non‐parametric procedure. Using extreme value theory we construct a natural semiparametric estimator of this quantile region and prove a refined consistency result. A simulation study clearly demonstrates the good performance of our estimator. We use the procedure for risk management by applying it to stock market returns.
Original languageEnglish
Pages (from-to)449-461
Number of pages13
JournalJournal of the Royal Statistical Society Series B-Statistical Methodology
Issue number2
Publication statusPublished - Mar 2017
Externally publishedYes


  • Extreme value statistics
  • Half-space depth
  • Multivariate quantile
  • Outlier detection
  • Rare event
  • Tail dependence

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