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Testing the independence of maxima: from bivariate vectors to spatial extreme fields: Asymptotic independence of extremes

机译：测试极大值的独立性：从二元向量到空间极限场：极限的渐近独立性

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摘要

Characterizing the behaviour of multivariate or spatial extreme values is of fundamental interest to understand how extreme events tend to occur. In this paper we propose to test for the asymptotic independence of bivariate maxima vectors. Our test statistic is derived from a madogram, a notion classically used in geostatistics to capture spatial structures. The test can be applied to bivariate vectors, and a generalization to the spatial context is proposed. For bivariate vectors, a comparison to the test by Falk and Michel (Ann Inst Stat Math 58:261-290, 2006) is conducted through a simulation study. In the spatial case, special attention is paid to pairwise dependence. A multiple test procedure is designed to determine at which lag asymptotic independence takes place. This new procedure is based on the bootstrap distribution of the number of times the null hypothesis is rejected. It is then tested on maxima of three classical spatial models and finally applied to two climate datasets.
机译：表征多元变量或空间极端值的行为对于了解极端事件倾向于如何发生至关重要。在本文中，我们建议测试二元最大值向量的渐近独立性。我们的测试统计量来自madogram，这是地统计学中通常用于捕获空间结构的概念。该检验可以应用于双变量向量，并且提出了对空间上下文的概括。对于双变量向量，通过模拟研究与Falk和Michel的测试（Ann Inst Stat Math 58：261-290，2006）进行了比较。在空间情况下，要特别注意成对依赖性。设计了多重测试程序来确定发生滞后渐近独立性的时间。此新过程基于无效假设被拒绝次数的自举分布。然后在三个经典空间模型的最大值上对其进行测试，最后将其应用于两个气候数据集。

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