Modelling the distribution of the cluster maxima of exceedances of subasymptotic thresholds
A standard approach to model the extreme values of a stationary process is the peaks over threshold method, which consists of imposing a high threshold, identifying clusters of exceedances of this threshold and fitting the maximum value from each cluster using the generalized Pareto distribution. Th...
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| Veröffentlicht in: | Biometrika 2012-03, Vol.99 (1), p.43-55 |
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| creator | EASTOE, EMMA F. TAWN, JONATHAN A. |
| description | A standard approach to model the extreme values of a stationary process is the peaks over threshold method, which consists of imposing a high threshold, identifying clusters of exceedances of this threshold and fitting the maximum value from each cluster using the generalized Pareto distribution. This approach is strongly justified by underlying asymptotic theory. We propose an alternative model for the distribution of the cluster maxima that accounts for the subasymptotic theory of extremes of a stationary process. This new distribution is a product of two terms, one for the marginal distribution of exceedances and the other for the dependence structure of the exceedance values within a cluster. We illustrate the improvement in fit, measured by the root mean square error of the estimated quantités, offered by the new distribution over the peaks over thresholds analysis using simulated and hydrological data, and we suggest a diagnostic tool to help identify when the proposed model is likely to lead to an improved fit. |
| doi_str_mv | 10.1093/biomet/asr078 |
| format | Article |
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| ispartof | Biometrika, 2012-03, Vol.99 (1), p.43-55 |
| issn | 0006-3444 1464-3510 |
| language | eng |
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| source | RePEc; JSTOR Mathematics & Statistics; Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current); Alma/SFX Local Collection |
| subjects | Applications Approximation Asymptotic methods Biology, psychology, social sciences Confidence interval Distribution theory Estimation bias Estimation methods Exact sciences and technology General topics Inference Mathematical maxima Mathematical models Mathematics Modeling Parametric models Pareto optimum Probability and statistics Probability distribution Probability theory and stochastic processes Reliability functions Sciences and techniques of general use Statistical models Statistics Stochastic processes Studies |
| title | Modelling the distribution of the cluster maxima of exceedances of subasymptotic thresholds |
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