Estimation of extreme depth-based quantile regions

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Consider the extreme quantile region induced by the half-space depth function HD of the form Q={x∈R^d ∶HD(x,P)≤β}, such that PQ = p 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
JournalJournal of the Royal Statistical Society, Series B
Volume79
Issue number2
DOIs
Publication statusPublished - Mar 2017

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

Cite this

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title = "Estimation of extreme depth-based quantile regions",
abstract = "Consider the extreme quantile region induced by the half-space depth function HD of the form Q={x∈R^d ∶HD(x,P)≤β}, such that PQ = p 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.",
author = "Yi He and John Einmahl",
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Estimation of extreme depth-based quantile regions. / He, Yi; Einmahl, John.

In: Journal of the Royal Statistical Society, Series B, Vol. 79, No. 2, 03.2017, p. 449-461.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Einmahl, John

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AB - Consider the extreme quantile region induced by the half-space depth function HD of the form Q={x∈R^d ∶HD(x,P)≤β}, such that PQ = p 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.

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DO - 10.1111/rssb.12163

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JO - Journal of the Royal Statistical Society, Series B

JF - Journal of the Royal Statistical Society, Series B

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