Asymptotic Domination of Sample Maxima

Enkelejd Hashorva (1) , Didier Rullière (2)

1 UNIL - Université de Lausanne = University of Lausanne
2 SAF - Laboratoire de Sciences Actuarielle et Financière

For a given random sample from some underlying multivariate distribution F we consider the domination of the component-wise maxima by some independent random vector W with underlying distribution function G. We show that the probability that certain components of the sample maxima are dominated by the corresponding components of W can be approximated under the assumptions that both F and G are in the max-domain of attraction of some max-stable distribution function F and G, respectively. We study further some basic properties of the dominated components of sample maxima by W .

Mots clés: Max-stable distributions; domination of sample maxima; extremal dependence; inf-argmax formula; de Haan representation; records

Domaines: Economies et finances; Probabilités [math.PR]; Statistiques [math.ST]

Enkelejd Hashorva, Didier Rullière. Asymptotic Domination of Sample Maxima. Statistics and Probability Letters, 2020, 160 (108703), ⟨10.1016/j.spl.2020.108703⟩. ⟨hal-02277020⟩