## The Annals of Statistics

### Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition

#### Abstract

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.

#### Article information

Source
Ann. Statist., Volume 34, Number 4 (2006), 1987-2014.

Dates
First available in Project Euclid: 3 November 2006

https://projecteuclid.org/euclid.aos/1162567640

Digital Object Identifier
doi:10.1214/009053606000000434

Mathematical Reviews number (MathSciNet)
MR2283724

Zentralblatt MATH identifier
1246.60051

#### Citation

Einmahl, John H. J.; de Haan, Laurens; Li, Deyuan. Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition. Ann. Statist. 34 (2006), no. 4, 1987--2014. doi:10.1214/009053606000000434. https://projecteuclid.org/euclid.aos/1162567640

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