Estimating a directed tree for extremes
Estimating a directed tree for extremes
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DOI：
10.1093/jrsssb/qkad165
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发表时间：
2021-02
期刊：
影响因子：
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通讯作者：
N. Tran;Johannes Buck;Claudia Klüppelberg
中科院分区：
文献类型：
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作者：
N. Tran;Johannes Buck;Claudia Klüppelberg
我们提出了一种从极端数据估计根向生成树的新方法。突出的例子是河流网络，可以通过在一组站点测量的极端流量来发现。我们的新算法利用最大线性贝叶斯网络的定性方面，该网络专为极端情况下的因果关系建模而设计。该算法估计双变量分数并返回根向生成树。它在基准数据和新数据上表现得非常好。我们证明新的估计量在带有噪声的最大线性贝叶斯网络模型下是一致的。我们还在小型模拟研究中评估了其优点和局限性。
We propose a new method to estimate a root-directed spanning tree from extreme data. Prominent example is a river network, to be discovered from extreme flow measured at a set of stations. Our new algorithm utilizes qualitative aspects of a max-linear Bayesian network, which has been designed for modelling causality in extremes. The algorithm estimates bivariate scores and returns a root-directed spanning tree. It performs extremely well on benchmark data and on new data. We prove that the new estimator is consistent under a max-linear Bayesian network model with noise. We also assess its strengths and limitations in a small simulation study.