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

• 成果类型: Article
• 署名作者: Einmahl, John H. J.; De Haan, Laurens; Li, Deyuan
• 署名单位: Tilburg University; University of Bern; Erasmus University Rotterdam; Erasmus University Rotterdam - Excl Erasmus MC
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000434
• 发表日期: 2006
• 页码: 1987-2014
• 关键词: dependence; CONVERGENCE; estimators; parameter

摘要

Consider n i.i.d. random vectors on 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.