Weighted Approximations of Tail Copula Processes with Application to Testing the Bivariate Extreme Value Condition
Consider n i.i.d. random vectors on ${\Bbb R}^{2}$ , 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 conditio...
| Veröffentlicht in: | The Annals of Statistics. - Institute of Mathematical Statistics. - 34(2006), 4, Seite 1987-2014 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2006
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| Zugriff auf das übergeordnete Werk: | The Annals of Statistics |
| Schlagworte: | Dependence structure Goodness-of-fit test Bivariate extreme value theory Tail copula process Weighted approximation Mathematics Philosophy |
| Zusammenfassung: | Consider n i.i.d. random vectors on ${\Bbb R}^{2}$ , 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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| ISSN: | 00905364 |