Abstract
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.
Funding Statement
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.
Acknowledgments
The authors are grateful to two referees and an Associate Editor for their constructive comments on an earlier version of this article which lead to a substantial improvements. They are particularly grateful for pointing out that Section 9.3 in Reiss (1989) provides some early results on the BM-method that do take care of the approximation error in the GEV approximation to block maxima.
Citation
Axel Bücher. Chen Zhou. "A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach." Statist. Sci. 36 (3) 360 - 378, August 2021. https://doi.org/10.1214/20-STS795
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