## Journal of Applied Probability

### Scaling of high-quantile estimators

#### Abstract

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.

#### Article information

Source
J. Appl. Probab., Volume 48, Number 4 (2011), 968-983.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046013

Digital Object Identifier
doi:10.1239/jap/1324046013

Mathematical Reviews number (MathSciNet)
MR2896662

Zentralblatt MATH identifier
1229.62139

Subjects
Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G32: Statistics of extreme values; tail inference

#### Citation

Degen, Matthias; Embrechts, Paul. Scaling of high-quantile estimators. J. Appl. Probab. 48 (2011), no. 4, 968--983. doi:10.1239/jap/1324046013. https://projecteuclid.org/euclid.jap/1324046013

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