Minimum distance estimation of Pickands dependence function for multivariate distributions
Minimum distance estimation of Pickands dependence function for multivariate distributions
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多元分布的 Pickands 依赖函数的最小距离估计
DOI：
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发表时间：
2012
期刊：
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通讯作者：
H. Dette
中科院分区：
文献类型：
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作者：
Betina Berghaus;Axel Bücher;H. Dette
我们考虑估计与多元分布相对应的 Pickands 依赖函数的问题。提出了一种基于经验和极值联结函数对数之间的 L2 距离的最小距离估计器。最小化器可以明确地表示为经验系函数对数的线性函数，并证明了相应过程在单纯形上的弱收敛性。与最近在文献中提出的用于多元 Pickands 依赖函数的非参数估计的其他程序相比 [参见Zhang 等人，2017]。 (2008) 和 Gudendorf 和 Segers (2011)]，本文构建的估计量不需要边际分布的知识，并且是 Gudendorf 和 Segers (2012) 最近提出的方法的替代方法。此外，最小距离方法允许为多元极值联结函数的假设构建简单的检验，这与广泛的替代方案是一致的。通过模拟研究研究了估计器的有限样本特性和乘法自举版本的测试。
We consider the problem of estimating the Pickands dependence function corresponding to a multivariate distribution. A minimum distance estimator is proposed which is based on a L2-distance between the logarithms of the empirical and an extreme-value copula. The minimizer can be expressed explicitly as a linear functional of the logarithm of the empirical copula and weak convergence of the corresponding process on the simplex is proved. In contrast to other procedures which have recently been proposed in the literature for the nonparametric estimation of a multivariate Pickands dependence function [see Zhang et al. (2008) and Gudendorf and Segers (2011)], the estimators constructed in this paper do not require knowledge of the marginal distributions and are an alternative to the method which has recently been suggested by Gudendorf and Segers (2012). Moreover, the minimum distance approach allows the construction of a simple test for the hypothesis of a multivariate extreme-value copula, which is consistent against a broad class of alternatives. The finite-sample properties of the estimator and a multiplier bootstrap version of the test are investigated by means of a simulation study.