A Semiparametric Bootstrap Technique for Simulating Extreme Order Statistics

Zelterman, Daniel

doi:10.2307/2290327

Cited by 9 publications

(15 citation statements)

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“…The null hypothesis in the KS test states that the two samples have similar empirical distribution functions and that there is no significant difference between them. For the boot strap samples of the same size as the original sample, the null hypothesis could not be rejected at α = 0.05, whereas using the semi-parametric approach of Zelterman (1993) the KS test suggested that the null hypothesis is rejected for all bootstrap samples. Therefore, bootstrap samples of the same size as the original sample population are used.…”

Section: Extreme Value Analysis and Uncertainty Estimatesmentioning

confidence: 95%

“…The literature on bootstrapping suggests that when re-sampling maxima or extreme order statistics (e.g. Zelterman, 1993;Shao and Tu, 1995), the size of a bootstrap sample should be smaller than that of the original sample. However, as the regionally pooled standardized SM distributions have relatively light tails, even though the generalized extreme value (GEV) distribution provides a good fit as proved by a quantile-quantile plot (not shown), a bootstrap sample of the same size as the original sample gives representative statistics for each region.…”

Section: Extreme Value Analysis and Uncertainty Estimatesmentioning

confidence: 99%

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Multi‐model ensemble estimates of climate change impacts on UK seasonal precipitation extremes

Fowler

Ekström

2009

Intl Journal of Climatology

214

182

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Thirteen regional climate model (RCM) integrations from the Prediction of Regional Scenarios and Uncertainties for Defining European Climate change risks and Effects (PRUDENCE) ensemble are used together with extreme value analysis to assess changes to seasonal precipitation extremes in nine UK rainfall regions by 2070-2100 under the SRES A2 emissions scenario. Model weights are based on similarities between observed and modelled UK extreme precipitation calculated for a combination of (1) spatial characteristics: the semi-variogram parameters sill and range, and (2) the discrepancy in the regional median seasonal maxima. These weights are used to combine individual RCM bootstrap samples to provide multi-model ensemble estimates of percent change in the return value magnitudes of regional extremes. The contribution of global climate model (GCM) and RCM combinations to model structural uncertainty is also investigated. The multi-model ensembles project increases across the UK in winter, spring and autumn extreme precipitation; although there is uncertainty in the absolute magnitude of increases, these range from 5 to 30% depending upon region and season. In summer, model predictions span the zero change line, although there is low confidence due to poor model performance. RCM performance is shown to be highly variable; extremes are well simulated in winter and very poorly simulated in summer. The ensemble distributions are wider (projections are more uncertain) for shorter duration extremes (e.g. 1 day) and higher return periods (e.g. 25 year). There are rather limited differences in the weighted and unweighted multi-model ensembles, perhaps a consequence of the lack of model independence between ensemble members. The largest contribution to uncertainty in the multi-model ensembles comes from the lateral boundary conditions used by RCMs included in the ensemble. Therefore, the uncertainty bounds shown here are conservative despite the relatively large number of RCMs contributing to the multi-model ensemble distribution.

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Section: Extreme Value Analysis and Uncertainty Estimatesmentioning

confidence: 95%

Section: Extreme Value Analysis and Uncertainty Estimatesmentioning

confidence: 99%

Multi‐model ensemble estimates of climate change impacts on UK seasonal precipitation extremes

Fowler

Ekström

2009

Intl Journal of Climatology

214

182

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“…Because our upper bounds involve an extreme order statistic (in particular the minimum of results from pairwise comparisons), standard bootstrapping methods are invalid. We instead use the bootstrapping method for extreme order statistics proposed by Zelterman (1993).…”

Section: Resultsmentioning

confidence: 99%

“…We defer a detailed discussion of the Zelterman (1993) bootstrap to Section 8.1. We chose to display a two-tailed 90% confidence interval because this allows easy visualization of the one-tailed test of whether the elasticity bound is less than 1 at the standard (5%) significance level.…”

Section: Resultsmentioning

confidence: 99%

Revealed Growth: A Method for Bounding the Elasticity of Demand with an Application to Assessing the Antitrust Remedy in the Du Pont Decision

Mullin

Snyder

2018

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, and seminar participants at the 2018 International Industrial Organization Conference (Indianapolis) for valuable discussions, to John Cocklin for insights on locating historical data sources, and to Marvin Lieberman and the Dartmouth FIVE Project for sharing their data on the chemicals industry. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications.

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“…(5) with the normalizing constants, aT and b T , specified by (6); (ii) the type Ill extreme value d.f. (1 1) with the shape parameter a determined by (12) and the normalizing constants by (13); and (iii) the exact d.f. of M T under independence (10).…”

Section: Approachmentioning

confidence: 99%

Sensitivity of extreme events to climate change: The case of autocorrelated time series

Katz

Brown

1994

Environmetrics

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SUMMARYThe relative sensitivity of an extreme event is defined as the partial derivative of its probability with respect to the location or scale parameter of the distribution of the variable involved. Of particular interest in climate applications are extreme events of the form, the maximum of a sequence of observations of the variable exceeding a threshold. In this case, the relative sensitivities are directly related to the hazard rate for the distribution of the maximum. By means of simulations, this hazard rate is determined for the maximum of a finite sequence of autocorrelated random variables. For large values, the hazard rate rises more steeply than the asymptotic theory based on the type I extreme value distribution would predict. Unless the degree of autocorrelation is quite high, the hazard rate does not differ much for large values from that for independent time series. The hazard rate for the so-called 'penultimate approximation', based on the type Ill extreme value distribution, is also compared to the exact hazard rate under dependence. These results imply that the relative sensitivity of extreme events to overall climate change is even greater than the asymptotic theory would predict. Time series of daily maximum temperature, data that possess substantial autocorrelation, are utilized for illustrative purposes. KEY WORDS Autoregressive processHazard rate Maximum Type I extreme value distribution

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A Semiparametric Bootstrap Technique for Simulating Extreme Order Statistics

Cited by 9 publications

References 0 publications

Multi‐model ensemble estimates of climate change impacts on UK seasonal precipitation extremes

Multi‐model ensemble estimates of climate change impacts on UK seasonal precipitation extremes

Revealed Growth: A Method for Bounding the Elasticity of Demand with an Application to Assessing the Antitrust Remedy in the Du Pont Decision

Sensitivity of extreme events to climate change: The case of autocorrelated time series

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