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Bootstrap simulations for evaluating the uncertainty associated with peaks‐over‐threshold estimates of extreme wind velocity
Author(s) -
Pandey M. D.,
Van Gelder P. H. A. J. M.,
Vrijling J. K.
Publication year - 2003
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.555
Subject(s) - quantile , parametric statistics , statistics , generalized pareto distribution , extreme value theory , econometrics , mathematics , wind speed , variance (accounting) , selection (genetic algorithm) , parametric model , computer science , meteorology , economics , physics , accounting , artificial intelligence
In the peaks‐over‐threshold (POT) method of extreme quantile estimation, the selection of a suitable threshold is critical to estimation accuracy. In practical applications, however, the threshold selection is not so obvious due to erratic variation of quantile estimates with minor changes in threshold. To address this issue, the article investigates the variation of quantile uncertainty (bias and variance) as a function of threshold using a semi‐parametric bootstrap algorithm. Furthermore, the article compares the performance of L‐moment and de Haan methods that are used for fitting the Pareto distribution to peak data. The analysis of simulated and actual U.S. wind speed data illustrates that the L‐moment method can lead to almost unbiased quantile estimates for certain thresholds. A threshold corresponding to minimum standard error appears to provide reasonable estimates of wind speed extremes. It is concluded that the quantification of uncertainty associated with a quantile estimate is necessary for selecting a suitable threshold and estimating the design wind speed. For this purpose, semi‐parametric bootstrap method has proved to be a simple, practical and effective tool. Copyright © 2003 John Wiley & Sons, Ltd.