Estimation of Extreme Depth-Based Quantile Regions

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Abstract

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
PublisherEconometrics
Number of pages24
Volume2014-035
Publication statusPublished - 29 May 2014

Publication series

NameCentER Discussion Paper
Volume2014-035

Fingerprint

Halfspace Depth
Quantile
Extremes
Extreme Quantiles
Estimator
Extreme Value Theory
Risk Management
Stock Market
Convex Hull
Simulation Study
Demonstrate

Keywords

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

Estimation of Extreme Depth-Based Quantile Regions. / He, Y.; Einmahl, J.H.J.

Tilburg : Econometrics, 2014. (CentER Discussion Paper; Vol. 2014-035).

Research output: Working paperDiscussion paperOther research output

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N2 - 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.

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He Y, Einmahl JHJ. Estimation of Extreme Depth-Based Quantile Regions. Tilburg: Econometrics. 2014 May 29. (CentER Discussion Paper).