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

Berman’s inequality under random scaling

Pages: 339 – 349

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n3.a4

Authors

Enkelejd Hashorva (Faculty of Business and Economics (HEC Lausanne), University of Lausanne, Switzerland)

Zhichao Weng (Faculty of Business and Economics (HEC Lausanne), University of Lausanne, Switzerland)

Abstract

Berman’s inequality is the key for establishing asymptotic properties of maxima of Gaussian random sequences and supremum of Gaussian random fields. This contribution shows that, asymptotically an extended version of Berman’s inequality can be established for randomly scaled Gaussian random vectors. Two applications presented in this paper demonstrate the use of Berman’s inequality under random scaling.

Keywords

Berman’s inequality, limit distribution, extremal index, random scaling, Hüsler-Reiss distribution

2010 Mathematics Subject Classification

Primary 60G15. Secondary 60G70.

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