Estimation of Extreme Depth-Based Quantile Regions

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Consider the extreme quantile region, induced by the halfspace depth function HD, of the form Q = fx 2 Rd : HD(x; P) g, such that PQ = p for a given, very small p > 0. This region can hardly be estimated through a fully nonparametric procedure since the sample halfspace depth is 0 outside the convex hull of the data. 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
Place of PublicationTilburg
Number of pages24
Publication statusPublished - 29 May 2014

Publication series

NameCentER Discussion Paper



  • Extreme value statistics
  • halfspace depth
  • multivariate quantile
  • outlier detection
  • rare event
  • tail dependence

Cite this

He, Y., & Einmahl, J. H. J. (2014). Estimation of Extreme Depth-Based Quantile Regions. (CentER Discussion Paper; Vol. 2014-035). Tilburg: Econometrics.