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August 2006 Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition
John H. J. Einmahl, Laurens de Haan, Deyuan Li
Ann. Statist. 34(4): 1987-2014 (August 2006). DOI: 10.1214/009053606000000434


Consider n i.i.d. random vectors on ℝ2, with unknown, common distribution function F. Under a sharpening of the extreme value condition on F, we derive a weighted approximation of the corresponding tail copula process. Then we construct a test to check whether the extreme value condition holds by comparing two estimators of the limiting extreme value distribution, one obtained from the tail copula process and the other obtained by first estimating the spectral measure which is then used as a building block for the limiting extreme value distribution. We derive the limiting distribution of the test statistic from the aforementioned weighted approximation. This limiting distribution contains unknown functional parameters. Therefore, we show that a version with estimated parameters converges weakly to the true limiting distribution. Based on this result, the finite sample properties of our testing procedure are investigated through a simulation study. A real data application is also presented.


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John H. J. Einmahl. Laurens de Haan. Deyuan Li. "Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition." Ann. Statist. 34 (4) 1987 - 2014, August 2006.


Published: August 2006
First available in Project Euclid: 3 November 2006

zbMATH: 1246.60051
MathSciNet: MR2283724
Digital Object Identifier: 10.1214/009053606000000434

Primary: 62G10 , 62G30 , 62G32
Secondary: 60F17 , 60G70

Keywords: bivariate extreme value theory , dependence structure , Goodness-of-fit test , tail copula process , weighted approximation

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 4 • August 2006
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