Testing for Bivariate Extreme Dependence Using Kendall's Process

New tests for the hypothesis of bivariate extreme-value dependence are proposed. All test statistics that are investigated are continuous functionals of either Kendall's process or its version with estimated parameters. The procedures considered are based on linear combinations of moments and o...

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Bibliographic Details
Published in:Scandinavian journal of statistics 2012-09, Vol.39 (3), p.497-514
Main Author: QUESSY, JEAN-FRANÇOIS
Format: Article
Language:English
Subjects:
Applied statistics
asymptotic local power
Asymptotic methods
Central limit theorem
copula
Datasets
Estimators
extreme-value dependence
Gaussian distributions
Integral transformations
Kendall's process
multiplier central limit theorem
Null hypothesis
Probabilities
Sample size
Statistical analysis
Studies
Uranium
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Summary:New tests for the hypothesis of bivariate extreme-value dependence are proposed. All test statistics that are investigated are continuous functionals of either Kendall's process or its version with estimated parameters. The procedures considered are based on linear combinations of moments and on Cramér-von Mises distances. A suitably adapted version of the multiplier central limit theorem for Kendall's process enables the computation of asymptotically valid p-values. The power of the tests is evaluated for small, moderate and large sample sizes, as well as asymptotically, under local alternatives. An illustration with a real data set is presented.
ISSN:0303-6898
1467-9469
DOI:10.1111/j.1467-9469.2011.00739.x