Non-parametric Bayesian inference on bivariate extremes
Non-parametric Bayesian inference on bivariate extremes
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DOI：
10.1111/j.1467-9868.2010.00770.x
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发表时间：
2011-01-01
影响因子：
5.8
通讯作者：
Segers, Johan
中科院分区：
文献类型：
--
作者：
Guillotte, Simon;Perron, Francois;Segers, Johan
二元极值分布吸引域中二元分布函数的尾部可以用其极值吸引子的尾部来近似。极值吸引子具有属于三参数族的边缘和依赖结构，其特征在于单位区间上的平均值等于1/2的概率测度，称为谱测度。推理是在贝叶斯框架中使用删失似然方法进行的。一个先验分布构造在一个无限维模型，该模型是在同一时间密集和计算管理。提出了一种跨维马尔可夫链蒙特卡罗算法，并证明了该算法收敛于后验分布。在模拟中，贝叶斯估计的频谱测量显示，比较有利的频率非参数估计。提供了一个丹麦火灾保险索赔的数据集的应用程序。
The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme value distribution may be approximated by that of its extreme value attractor. The extreme value attractor has margins that belong to a three-parameter family and a dependence structure which is characterized by a probability measure on the unit interval with mean equal to 1/2, which is called the spectral measure. Inference is done in a Bayesian framework using a censored likelihood approach. A prior distribution is constructed on an infinite dimensional model for this measure, the model being at the same time dense and computationally manageable. A trans-dimensional Markov chain Monte Carlo algorithm is developed and convergence to the posterior distribution is established. In simulations, the Bayes estimator for the spectral measure is shown to compare favourably with frequentist non-parametric estimators. An application to a data set of Danish fire insurance claims is provided.