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Liujun Chen, Deyuan Li, Chen Zhou, Distributed inference for the extreme value index, Biometrika, Volume 109, Issue 1, March 2022, Pages 257–264, https://doi.org/10.1093/biomet/asab001
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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.