Domination of sample maxima and related extremal dependence measures

Author:

Hashorva Enkelejd1

Affiliation:

1. 1Department of Actuarial Science University of Lausanne, UNIL-Dorigny, 1015 Lausanne, Switzerland

Abstract

AbstractFor a given d-dimensional distribution function (df) H we introduce the class of dependence measures μ(H, Q) = −E{n H(Z1, . . . , Zd)}, where the random vector (Z1, . . . , Zd) has df Q which has the same marginal dfs as H. If both H and Q are max-stable dfs, we show that for a df F in the max-domain of attraction of H, this dependence measure explains the extremal dependence exhibited by F. Moreover, we prove that μ(H, Q) is the limit of the probability that the maxima of a random sample from F is marginally dominated by some random vector with df in the max-domain of attraction of Q. We show a similar result for the complete domination of the sample maxima which leads to another measure of dependence denoted by λ(Q, H). In the literature λ(H, H), with H a max-stable df, has been studied in the context of records, multiple maxima, concomitants of order statistics and concurrence probabilities. It turns out that both μ(H, Q) and λ(Q, H) are closely related. If H is max-stable we derive useful representations for both μ(H, Q) and λ(Q, H). Our applications include equivalent conditions for H to be a product df and F to have asymptotically independent components.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Modeling and Simulation,Statistics and Probability

Reference24 articles.

1. of Extremes;Beirlant;Statistics,2004

2. a Asymptotics of dominated Gaussian maxima Extremes;Hashorva,2002

3. Max - stable random sup - measures with comonotonic tail dependence Stochastic Process;Molchanov;Appl,2016

4. The tail process revisited Extremes to appear Available at https org;Planinic,2018

5. Multiple maxima in multivariate samples;Hashorva,2005

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Asymptotic domination of sample maxima;Statistics & Probability Letters;2020-05

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