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Name: Liujun Chen

Talk Title: Distributed Inference for Extreme Value Index

Abstract: 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, establish its asymptotic theories and provide sufficient, sometimes also necessary, condition, under which the oracle property holds.

In applications, estimates based on the distributed Hill estimator can be sensitive to the choice of the number of the exceedance ratios used in each machine. Even with choosing the number at a low level, a high asymptotic bias may arise. We overcome this potential drawback by designing a bias correction procedure for the distributed Hill estimator, adhere to the setup of distributed inference. The asymptotically unbiased distributed estimator we obtained, on the one hand, is applicable for the distributed data, on the other hand, inherits all known advantages of bias correction methods in extreme value statistics.

This talk is a contributed talk at EVA 2021.