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PREDICTIVE PERFORMANCE ANALYSIS OF PEAKS-OVER-THRESHOLD APPROACH WITHOUT-OF-BAG ESTIMATE
Keywords:
out-of-bag estimate, Newton-Raphson method, maximum likelihood estimator, extreme values theory, generalized Pareto distributionDOI:
https://doi.org/10.17654/0972086325017Abstract
In this paper, we propose an integrated approach combining graphical and analytical methods to select the optimal threshold and estimate the scale and shape parameters. For each threshold in the range of admissible thresholds derived from the graphical Hill and mean-excess methods, we estimate the scale and shape parameters of the generalized Pareto distribution (GPD) using a procedure combining the out-of-bag estimation (OOBE) with a modified Newton-Raphson numerical optimization algorithm. This numerical method uses a penalized log likelihood function. The numerical results for sample size 100 at 2000 show the reduction in the estimation bias. The proposed method is efficient than that of non-parametric approaches used by Hill and Smooth Hill estimators in terms of accuracy, as proven by numerical experiments and application to real river database obtained from the Lobo and Yzeron stations. These results show the good predictive performance of the OOBE method combined with a modified Newton-Raphson numerical optimization algorithm.
Received: July 28, 2025
Accepted: September 4, 2025
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