Summary In this paper we investigate a divide-and-conquer algorithm for estimating the extreme value index when data are stored in multiple machines. The oracle property of such an algorithm based on extreme value methods is not guaranteed by the general theory of distributed inference. We propose a distributed Hill estimator and establish its asymptotic theories. We consider various cases where the number of observations involved in each machine can be either homogeneous or heterogeneous, and either fixed or varying according to the total sample size. In each case we provide a sufficient, sometimes also necessary, condition under which the oracle property holds.

中文翻译：

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极值指数的分布式推理

总结 在本文中，我们研究了一种分治算法，用于在数据存储在多台机器中时估计极值指数。这种基于极值方法的算法的预言属性并不能由分布式推理的一般理论来保证。我们提出了一个分布式希尔估计器并建立了它的渐近理论。我们考虑了各种情况，其中每台机器中涉及的观察数量可以是同质的或异质的，并且根据总样本量是固定的或变化的。在每种情况下，我们都提供了一个充分的，有时也是必要的条件，在该条件下，oracle 属性保持不变。