Statistics and Its Interface

Volume 7 (2014)

Number 3

Special Issue on Extreme Theory and Application (Part I)

Guest Editors: Yazhen Wang and Zhengjun Zhang

Gaussian approximation of perturbed chi-square risks

Pages: 363 – 373

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n3.a6

Authors

Krzysztof Debicki (Mathematical Institute, University of Wrocław, Poland)

Enkelejd Hashorva (Department of Actuarial Science, University of Lausanne, Switzerland)

Lanpeng Ji (Department of Actuarial Science, University of Lausanne, Switzerland)

Abstract

In this paper we show that the conditional distribution of perturbed chi-square risks can be approximated by certain distributions including the Gaussian distributions. Our results are of interest for conditional extreme value models and multivariate extremes as shown in three applications.

Keywords

Gaussian approximation, chi-square distribution, Berman’s sojourn limit theorem, conditional limit law, Hüsler-Reiss distribution

2010 Mathematics Subject Classification

Primary 60G15. Secondary 60G70.

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