A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach

A Buecher, Chen Zhou

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)


Classical extreme value statistics consists of two fundamental approaches: the block maxima (BM) method and the peak-over-threshold (POT) approach. It seems to be general consensus among researchers in the field that the POT approach makes use of extreme observations more efficiently than the BM method. We shed light on this discussion from three different perspectives. First, based on recent theoretical results for the BM method, we provide a theoretical comparison in i.i.d. scenarios. We argue that the data generating process may favour either one or the other approach. Second, if the underlying data possesses serial dependence, we argue that the choice of a method should be primarily guided by the ultimate statistical interest: for instance, POT is preferable for quantile estimation, while BM is preferable for return level estimation. Finally, we discuss the two approaches for multivariate observations and identify various open ends for future research.
Original languageEnglish
Pages (from-to)360-378
Number of pages19
JournalStatistical Science
Issue number3
Publication statusPublished - Aug 2021

Bibliographical note

Funding Information:
Axel Bücher’s research has been supported by the Collaborative Research Center “Statistical modeling of nonlinear dynamic processes” (SFB 823) of the German Research Foundation, which is gratefully acknowledged.

Publisher Copyright:
© 2021. Institute of Mathematical Statistics.


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