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Estimation of extreme depth-based quantile regions

He,Yi
; 
Einmahl,John
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.
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2017-03
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Tilburg University Research Output Collection
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He, Y & Einmahl, J 2017, 'Estimation of extreme depth-based quantile regions', Journal of the Royal Statistical Society Series B-Statistical Methodology, vol. 79, no. 2, pp. 449-461. https://doi.org/10.1111/rssb.12163
URI
https://hdl.handle.net/20.500.14602/64203
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