Adapting the Hill estimator to distributed inference: dealing with the bias

Liujun Chen, Deyuan Li*, Chen Zhou

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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The distributed Hill estimator is a divide-and-conquer algorithm for estimating the extreme value index when data are stored in multiple machines. 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 when 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, which adheres to the setup of distributed inference. The asymptotically unbiased distributed estimator we obtained, on the one hand, is applicable to distributed stored data, on the other hand, inherits all known advantages of bias correction methods in extreme value statistics.

Original languageEnglish
Pages (from-to)389-416
Number of pages28
Issue number3
Early online date7 May 2022
Publication statusPublished - Sept 2022

Bibliographical note

Acknowledgement:s We thank the editors and three referees for their helpful comments and suggestions.
Liujun Chen and Deyuan Li’s research is partially supported by the National Nature Science Foundations of
China grants 11971115 and 71661137005.

Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


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