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

Convergence rate of maxima of bivariate Gaussian arrays to the Hüsler-Reiss distribution

Pages: 351 – 362

DOI: http://dx.doi.org/10.4310/SII.2014.v7.n3.a5

Authors

Xin Liao (Department of Statistics, School of Mathematics and Statistics, Southwest University, Chongqing, China)

Zuoxiang Peng (Department of Statistics, School of Mathematics and Statistics, Southwest University, Chongqing, China)

Abstract

The limit distribution of maxima formed by a triangular array of independent and identically distributed bivariate Gaussian random vectors is the Hüsler-Reiss max-stable distribution if and only if the correlation of each vector approaches one with a certain rate. In this paper, we introduce a second-order condition on the convergence rate of this correlation. Under this condition we derive the uniform convergence rate of the distribution of normalized bivariate maxima to its ultimate limit distribution.

Keywords

bivariate Gaussian random vector, Hüsler-Reiss max-stable distribution, maximum, uniform convergence rate

2010 Mathematics Subject Classification

Primary 60G70, 62E20. Secondary 60F05, 60F15.

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