Statistics and Its Interface
Volume 7 (2014)
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
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.
bivariate Gaussian random vector, Hüsler-Reiss max-stable distribution, maximum, uniform convergence rate
2010 Mathematics Subject Classification
Primary 60G70, 62E20. Secondary 60F05, 60F15.