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Scaling of High-Quantile Estimators

Part of: Nonparametric inference Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Matthias Degen  and
Paul Embrechts
Matthias Degen*
Affiliation:
ETH Zürich
Paul Embrechts*
Affiliation:
ETH Zürich and Swiss Finance Institute
*
∗ Postal address: Department of Mathematics, ETH Zürich, Raemistrasse 101, CH-8092 Zürich, Switzerland.
∗ Postal address: Department of Mathematics, ETH Zürich, Raemistrasse 101, CH-8092 Zürich, Switzerland.
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Abstract

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Enhanced by the global financial crisis, the discussion about an accurate estimation of regulatory (risk) capital a financial institution needs to hold in order to safeguard against unexpected losses has become highly relevant again. The presence of heavy tails in combination with small sample sizes turns estimation at such extreme quantile levels into an inherently difficult statistical issue. We discuss some of the problems and pitfalls that may arise. In particular, based on the framework of second-order extended regular variation, we compare different high-quantile estimators and propose methods for the improvement of standard methods by focusing on the concept of penultimate approximations.

Keywords

Extreme value theorypeaks over thresholdpenultimate approximationpower normalizationsecond-order extended regular variation

MSC classification

Secondary: 60G70: Extreme value theory; extremal processes 62G32: Statistics of extreme values; tail inference
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 968 - 983
Copyright
Copyright © Applied Probability Trust 2011 

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