Asymptotics of joint maxima for discontinuous random variables

A. Feidt; Christian Genest; Johana Nešlehová

doi:10.1007/s10687-009-0085-7

Asymptotics of joint maxima for discontinuous random variables

A. Feidt, Christian Genest, Johana Nešlehová^*

^*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Wissenschaftliche Fachzeitschrift › Originalbeitrag in Fachzeitschrift › Begutachtung

Abstract

This paper explores the joint extreme-value behavior of discontinuous random variables. It is shown that as in the continuous case, the latter is characterized by the weak limit of the normalized componentwise maxima and the convergence of any compatible copula. Illustrations are provided and an extension to the case of triangular arrays is considered which sheds new light on recent work of Coles and Pauli (Stat Probab Lett 54:373-379, 2001) and Mitov and Nadarajah (Extremes 8:357-370, 2005). This leads to considerations on the meaning of the bivariate upper tail dependence coefficient of Joe (Comput Stat Data Anal 16:279-297, 1993) in the discontinuous case.

Originalsprache	Englisch
Seiten (von - bis)	35-53
Seitenumfang	19
Fachzeitschrift	Extremes
Jahrgang	13
Ausgabenummer	1
DOIs	https://doi.org/10.1007/s10687-009-0085-7
Publikationsstatus	Veröffentlicht - Feb. 2010
Extern publiziert	Ja

Bibliographische Notiz

Funding Information:
Acknowledgements Funding in partial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada, the Fonds québécois de la recherche sur la nature et les technologies, the Institut de finance mathématique de Montréal, and the Swiss National Science Foundation.

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