Weighted approximations of tail copula processes with application to testing the bivariate extreme value condition
研究了在极值条件下尾部Copula过程的加权逼近，并基于此构造了一个检验二元极值条件是否成立的统计方法，通过模拟和实际数据验证了其有限样本性质。
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.