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Limit laws for extremes of dependent stationary Gaussian arrays

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Publication date 2013
Author Hashorva Enkelejd, Weng Zhichao,
Project Extremal Behaviour of Random Scaling Models
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Original article (peer-reviewed)

Journal Statistics and Probability, Letters
Volume (Issue) 83
Page(s) 320 - 330
Title of proceedings Statistics and Probability, Letters
DOI 10.1016/j.spl.2012.09.017

Abstract

In this paper we show that the componentwise maxima of weakly dependent bivariate stationary Gaussian triangular arrays converge in distribution after appropriate normalization to Hüsler–Reiss distribution. Under a strong dependence assumption, we prove that the limit distribution of the maxima is a mixture of a bivariate Gaussian distribution and Hüsler–Reiss distribution. An important new finding of our paper is that the componentwise maxima and componentwise minima remain asymptotically independent even in the settings of Hüsler and Reiss (1989) allowing further for weak dependence. Further we derive an almost sure limit theorem under the Berman condition for the components of the triangular array.
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