Abstract
A common statistical problem in hydrology is the estimation of annual maximal river flow distributions and their quantiles, with the objective of evaluating flood protection systems. Typically, record lengths are short and estimators imprecise, so that it is advisable to exploit additional sources of information. However, there is often uncertainty about the adequacy of such information, and a strict decision on whether to use it is difficult. We propose penalized quasi-maximum likelihood estimators to overcome this dilemma, allowing one to push the model towards a reasonable direction defined a priori. We are particularly interested in regional settings, with river flow observations collected at multiple stations. To account for regional information, we introduce a penalization term inspired by the popular Index Flood assumption. Unlike in standard approaches, the degree of regionalization can be controlled gradually instead of deciding between a local or a regional estimator. Theoretical results on the consistency of the estimator are provided and extensive simulations are performed for the reason of comparison with other local and regional estimators. The proposed procedure yields very good results, both for homogeneous as well as for heterogeneous groups of sites. A case study consisting of sites in Saxony, Germany, illustrates the applicability to real data.
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Acknowledgements
Open Access funding provided by Projekt DEAL. The authors are grateful to the associate editor and two anonymous referees, whose comments on an earlier version of this manuscript lead to a significant improvement. Furthermore, the authors would like to thank Professor Andreas Schumann and his research group from the Department of Civil Engineering, Ruhr-University Bochum, Germany, for supplying the data used in the Case Study. Financial support of the Deutsche Forschungsgemeinschaft (SFB 823) is gratefully acknowledged.
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Bücher, A., Lilienthal, J., Kinsvater, P. et al. Penalized quasi-maximum likelihood estimation for extreme value models with application to flood frequency analysis. Extremes 24, 325–348 (2021). https://doi.org/10.1007/s10687-020-00379-y
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DOI: https://doi.org/10.1007/s10687-020-00379-y
Keywords
- Regionalization
- Index flood assumption
- Generalized extreme value distribution
- Consistency with rate
- Tuning parameter selection