Nonparametric estimation of an extreme-value copula in arbitrary dimensions
Nonparametric estimation of an extreme-value copula in arbitrary dimensions
复制标题
DOI：
10.1016/j.jmva.2010.07.011
复制
发表时间：
2011-01-01
影响因子：
1.6
通讯作者：
Segers, Johan
中科院分区：
文献类型：
--
作者：
Gudendorf, Gordon;Segers, Johan
极值copula的推导通常通过它的Pickands依赖函数进行，Pickands依赖函数是单位单纯形上满足一定不等式约束的凸函数。在i.i.d.的设置中。对于来自具有已知边缘和未知极值copula的多元分布的随机样本，D. Zhang，M. T.威尔斯和L Peng [多元极值分布的依赖函数的非参数估计，多元分析杂志99（4）（2008）577-588]。没有给出估计量作为单纯形上的随机函数的联合渐近分布。此外，该估计的实现需要在单纯形上选择多个权函数，而权函数的最优选择问题尚未得到解决.结合标准经验过程理论，给出了一种新的简化的CFG估计表示，从而揭示了其在单纯形上连续实值函数空间中的渐近分布.此外，在一定的线性回归模型中的截距的普通最小二乘估计提供了一个自适应版本的CFG估计，其渐近行为是相同的，如果方差最小化的权重函数被使用。如模拟研究所示，效率的提高可以相当可观。(C)2010年爱思唯尔公司All rights reserved.
Inference on an extreme-value copula usually proceeds via its Pickands dependence function, which is a convex function on the unit simplex satisfying certain inequality constraints. In the setting of an i.i.d. random sample from a multivariate distribution with known margins and an unknown extreme-value copula, an extension of the Caperaa-Fougeres-Genest estimator was introduced by D. Zhang, M. T. Wells and L Peng [Nonparametric estimation of the dependence function for a multivariate extreme-value distribution, journal of Multivariate Analysis 99 (4) (2008) 577-588]. The joint asymptotic distribution of the estimator as a random function on the simplex was not provided. Moreover, implementation of the estimator requires the choice of a number of weight functions on the simplex, the issue of their optimal selection being left unresolved.A new, simplified representation of the CFG-estimator combined with standard empirical process theory provides the means to uncover its asymptotic distribution in the space of continuous, real-valued functions on the simplex. Moreover, the ordinary least-squares estimator of the intercept in a certain linear regression model provides an adaptive version of the CFG-estimator whose asymptotic behavior is the same as if the variance-minimizing weight functions were used. As illustrated in a simulation study, the gain in efficiency can be quite sizable. (C) 2010 Elsevier Inc. All rights reserved.