Minima and maxima of elliptical arrays and spherical processes

• Published in: Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 19; no. 3; pp. 886 - 904
• Main Author: HASHORVA, ENKELEJD
• Format: Journal Article
• Language: English
• Published: International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability 01-08-2013; Bernoulli Society for Mathematical Statistics and Probability
• Subjects: Asymptotic value; asymptotics of sample maxima; Brown–Resnick copula; Brown–Resnick process; Davis–Resnick tail property; Distribution functions; Gaussian process; Mathematical maxima; Mathematical minima; Mathematical theorems; Matrices; Penrose–Kabluchko process; Perceptron convergence procedure; Random variables; spherical process; Stochastic processes
• ISSN: 1350-7265
• DOI: 10.3150/12-BEJ463

In this paper, we investigate first the asymptotics of the minima of elliptical triangular arrays. Motivated by the findings of Kabluchko (Extremes 14 (2011) 285—310), we discuss further the asymptotic behaviour of the maxima of elliptical triangular arrays with marginal distribution functions in the Gumbel or Weibull max-domain of attraction. We present an application concerning the asymptotics of the maximum and the minimum of independent spherical processes.