Limit laws for extremes of dependent stationary Gaussian arrays

Enkelejd Hashorva and Zhichao Weng

Statistics & Probability Letters, 2013, vol. 83, issue 1, 320-330

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.

Keywords: Hüsler–Reiss distribution; Brown–Resnick copula; Gumbel max-domain of attraction; Berman condition; Almost sure limit theorem (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:83:y:2013:i:1:p:320-330

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DOI: 10.1016/j.spl.2012.09.017

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