Tests of symmetry for bivariate copulas

Christian Genest; Johanna Nešlehová; Jean François Quessy

doi:10.1007/s10463-011-0337-6

Tests of symmetry for bivariate copulas

Christian Genest^*, Johanna Nešlehová, Jean François Quessy

^*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Wissenschaftliche Fachzeitschrift › Originalbeitrag in Fachzeitschrift › Forschung › Begutachtung

Abstract

Tests are proposed for the hypothesis that the underlying copula of a continuous random pair is symmetric. The procedures are based on Cramér-von Mises and Kolmogorov-Smirnov functionals of a rank-based empirical process whose large-sample behaviour is obtained. The asymptotic validity of a re-sampling method to compute P values is also established. The technical arguments supporting the use of a Chi-squared test due to Jasson are also presented. A power study suggests that the proposed tests are more powerful than Jasson's procedure under many scenarios of copula asymmetry. The methods are illustrated on a nutrient data set.

Originalsprache	Englisch
Seiten (von - bis)	811-834
Seitenumfang	24
Fachzeitschrift	Annals of the Institute of Statistical Mathematics
Jahrgang	64
Ausgabenummer	4
DOIs	https://doi.org/10.1007/s10463-011-0337-6
Publikationsstatus	Veröffentlicht - Aug. 2012
Extern publiziert	Ja

Bibliographische Notiz

Funding Information:
Acknowledgments Funding from the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada, the Fonds québécois de la recherche sur la nature et les technologies, and the Fonds institutionnel de la recherche de l’Université du Québec à Trois-Rivières is gratefully acknowledged.

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abstract = "Tests are proposed for the hypothesis that the underlying copula of a continuous random pair is symmetric. The procedures are based on Cram{\'e}r-von Mises and Kolmogorov-Smirnov functionals of a rank-based empirical process whose large-sample behaviour is obtained. The asymptotic validity of a re-sampling method to compute P values is also established. The technical arguments supporting the use of a Chi-squared test due to Jasson are also presented. A power study suggests that the proposed tests are more powerful than Jasson's procedure under many scenarios of copula asymmetry. The methods are illustrated on a nutrient data set.",

keywords = "Empirical copula process, Exchangeability, Multiplier Central Limit Theorem, Ranks, Symmetry",

author = "Christian Genest and Johanna Ne{\v s}lehov{\'a} and Quessy, {Jean Fran{\c c}ois}",

note = "Funding Information: Acknowledgments Funding from the Canada Research Chairs Program, the Natural Sciences and Engineering Research Council of Canada, the Fonds qu{\'e}b{\'e}cois de la recherche sur la nature et les technologies, and the Fonds institutionnel de la recherche de l{\textquoteright}Universit{\'e} du Qu{\'e}bec {\`a} Trois-Rivi{\`e}res is gratefully acknowledged.",

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