Generalized pareto regression trees for extreme event analysis

This paper derives finite sample results to assess the consistency of Generalized Pareto regression trees introduced by Farkas et al. (Insur. Math. Econ. 98:92–105,  2021 ) as tools to perform extreme value regression for heavy-tailed distributions. This procedure allows the constitution of classes...

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Bibliographic Details
Published in:Extremes (Boston) 2024-09, Vol.27 (3), p.437-477
Main Authors: Farkas, Sébastien, Heranval, Antoine, Lopez, Olivier, Thomas, Maud
Format: Article
Language:English
Subjects:
Algorithms
Behavior
Civil Engineering
Economics
Environmental Management
Extreme values
Finance
Goodness of fit
Hydrogeology
Insurance
Management
Mathematics and Statistics
Natural disasters
Neural networks
Quality Control
Regression analysis
Regression models
Reliability
Safety and Risk
Statistics
Statistics for Business
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Summary:This paper derives finite sample results to assess the consistency of Generalized Pareto regression trees introduced by Farkas et al. (Insur. Math. Econ. 98:92–105,  2021 ) as tools to perform extreme value regression for heavy-tailed distributions. This procedure allows the constitution of classes of observations with similar tail behaviors depending on the value of the covariates, based on a recursive partition of the sample and simple model selection rules. The results we provide are obtained from concentration inequalities, and are valid for a finite sample size. A misspecification bias that arises from the use of a “Peaks over Threshold” approach is also taken into account. Moreover, the derived properties legitimate the pruning strategies, that is the model selection rules, used to select a proper tree that achieves a compromise between simplicity and goodness-of-fit. The methodology is illustrated through a simulation study, and a real data application in insurance for natural disasters.
ISSN:1386-1999
1572-915X
DOI:10.1007/s10687-024-00485-1