Statistics and Its Interface
Volume 7 (2014)
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
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.
Berman’s inequality, limit distribution, extremal index, random scaling, Hüsler-Reiss distribution
2010 Mathematics Subject Classification
Primary 60G15. Secondary 60G70.