Abstract
The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding rather than disjoint block maxima. Similar results are derived for general non-degenerate U-statistics of arbitrary order, in the multivariate time series case. Details are worked out for selected examples: the empirical variance, the probability weighted moment estimator and Kendall’s tau statistic. The results are also extended to the case where the underlying sample is piecewise stationary. The finite-sample properties are illustrated by a Monte Carlo simulation study.
Funding Statement
This work has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), DFG project 465665892, which is gratefully acknowledged.
Acknowledgments
The authors are grateful to two unknown referees and an associate editor for their constructive comments that helped to improve the presentation substantially. The authors also appreciate valuable comments by multiple participants of the Extreme Value Analysis (EVA) Conference in Milano in 2023.
Citation
Axel Bücher. Torben Staud. "Limit theorems for non-degenerate U-statistics of block maxima for time series." Electron. J. Statist. 18 (2) 2850 - 2885, 2024. https://doi.org/10.1214/24-EJS2269
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