scholarly journals Comments on “Plotting Positions in Extreme Value Analysis”

2011 ◽  
Vol 50 (1) ◽  
pp. 255-266 ◽  
Author(s):  
Nicholas Cook
Keyword(s):  
Sampling Error ◽  
Extreme Value ◽  
Building Codes ◽  
Extreme Value Analysis ◽  
Model Parameters ◽  
Value Analysis ◽  
Opposite Case ◽  
Past Half Century ◽  
Unique Status

Abstract This comment addresses the role of sampling error in extreme value analysis. A note published in this journal claimed that Weibull’s 1939 estimator for sample probability has a unique status that invalidates all other estimators and renders invalid all of the developments of unbiased distribution-dependent estimators made since 1939. The note concluded that the use of distribution-dependent estimators should be abandoned and that many estimates of the weather-related risks should be reevaluated and the related building codes and other related regulations updated. This comment uses rigorous statistical proofs to make the diametrically opposite case: namely, that development of distribution-dependent estimators has resulted in an improvement in accuracy over the past half century and that no changes are required to the basis of weather-related building codes and regulations. These rigorous proofs are supplemented by sampling experiments that demonstrate their validity. This comment provides an introduction to the basic statistical concepts of the statistical modeling of extremes, including unbiased estimators for the model parameters.

Future European changes of extreme precipitation : What can we learn from inter-model cross-validation?

2020 ◽  
Author(s):  
Torben Schmith ◽  
Peter Thejll ◽  
Fredrik Boberg ◽  
Peter Berg ◽  
Ole Bøssing Christensen ◽  
...  
Keyword(s):  
Error Correction ◽  
Cross Validation ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Return Levels ◽  
Hourly Data ◽  
Calibration Techniques ◽  
Precipitation Events

<p>Severe precipitation events occur rarely and are often localized in space and of short duration, but are important for societal managing of infrastructure such as sewage systems, metros etc. Therefore, there is a demand for estimating expected future changes in the statistics of these rare events. These are usually projected using RCM scenario runs combined with extreme value analysis to obtain selected return levels of precipitation intensity. However, due to RCM imperfections, the modelled climate for the present-day usually has errors relative to observations. Therefore, the RCM results are ‘error corrected‘ to match observations more closely in order to increase reliability of results.</p><p>In the present work we evaluate different error correction techniques and compare with non-corrected projections. This is done in an inter-model cross-validation setup, in which each model in turn plays the role of observations, against which the remaining error-corrected models are validated. The study uses hourly data (historical & RCP8.5 late 21<sup>st</sup> century) from 13 models covering the EURO-CORDEX ensemble at 0.11 degree resolution (about 12.5 km), from which fields of selected return levels are extracted for 1 h and 24 h duration. The error correction techniques applied to the return levels are based on extreme value analysis and include analytical quantile-quantile matching together with a simpler climate factor approach.</p><p>The study identifies regions where the error correction techniques perform differently, and therefore contributes to guidelines on how and where to apply calibration techniques when projecting extreme return levels.</p>

Robust extreme value analysis: the bulk matching method

2020 ◽  
Author(s):  
Frank Kwasniok
Keyword(s):  
Exponential Family ◽  
Pareto Distribution ◽  
Likelihood Function ◽  
Atmospheric Model ◽  
Extreme Value ◽  
Extreme Value Analysis ◽  
High Threshold ◽  
Model Parameters ◽  
Value Analysis ◽  
Block Maxima

<p>Traditional extreme value analysis based on the generalised ex-<br>treme value (GEV) or generalised Pareto distribution (GPD) suffers<br>from two drawbacks: (i) Both methods are wasteful of data as only<br>block maxima or exceedances over a high threshold are taken into ac-<br>count and the bulk of the data is disregarded. (ii) Moreover, in the<br>GPD approach, there is no systematic way to determine the threshold<br>parameter. Here, all the data are fitted simultaneously using a gener-<br>alised exponential family model for the bulk and a GPD model for the<br>tail. At the threshold, the two distributions are linked together with<br>appropriate matching conditions. The model parameters are estimated<br>from the likelihood function of all the data. Also the threshold param-<br>eter can be determined via maximum likelihood in an outer loop. The<br>method is exemplified on wind speed data from an atmospheric model.</p>

scholarly journals Reply

2011 ◽  
Vol 50 (1) ◽  
pp. 267-270 ◽  
Author(s):  
Lasse Makkonen
Keyword(s):  
Order Statistics ◽  
Sampling Error ◽  
Extreme Weather ◽  
Extreme Value ◽  
Extreme Weather Events ◽  
Extreme Value Analysis ◽  
Exact Probability ◽  
Value Analysis ◽  
Weather Events

Abstract This reply addresses the use of order statistics in extreme value analysis. The author has previously proposed in this journal that the distribution-dependent estimators of plotting position in extreme value analysis should be abandoned and replaced by the Weibull formula. It was also demonstrated that the use of the wrong plotting positions has resulted in underestimation of the probability of extreme-weather events. Cook’s comments challenge these developments and defend the previously presented plotting methods. In this reply it is outlined that the Weibull formula provides the exact probability PI of nonexceedance in order-ranked data. Hence, there is no sampling error related to PI. This renders Cook’s primary arguments invalid. The specific critical comments by Cook are also replied to and are shown to be unfounded.

Modeling European hot spells using extreme value analysis

2014 ◽  
Vol 58 (3) ◽  
pp. 193-207 ◽  
Author(s):  
C Photiadou ◽  
MR Jones ◽  
D Keellings ◽  
CF Dewes
Keyword(s):  
Extreme Value ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Hot Spells

scholarly journals Threshold selection in univariate extreme value analysis

Extremes ◽  
2021 ◽  
Author(s):  
Laura Fee Schneider ◽  
Andrea Krajina ◽  
Tatyana Krivobokova
Keyword(s):  
Mean Squared Error ◽  
Extreme Value ◽  
Hill Estimator ◽  
Small Samples ◽  
Extreme Value Analysis ◽  
Threshold Selection ◽  
Value Analysis ◽  
Wide Range ◽  
Asymptotic Mean Squared Error ◽  
The Hill

AbstractThreshold selection plays a key role in various aspects of statistical inference of rare events. In this work, two new threshold selection methods are introduced. The first approach measures the fit of the exponential approximation above a threshold and achieves good performance in small samples. The second method smoothly estimates the asymptotic mean squared error of the Hill estimator and performs consistently well over a wide range of processes. Both methods are analyzed theoretically, compared to existing procedures in an extensive simulation study and applied to a dataset of financial losses, where the underlying extreme value index is assumed to vary over time.

Spatial stochastic simulation to aid local extreme value analysis of cyclone-induced wave heights when numerical hydrodynamic simulations are scarce

2021 ◽  
Author(s):  
Jeremy Rohmer ◽  
Rodrigo Pedreros ◽  
Yann Krien
Keyword(s):  
Confidence Interval ◽  
Stochastic Simulation ◽  
Extreme Value ◽  
Return Level ◽  
Extreme Value Analysis ◽  
Percentage Error ◽  
Value Analysis ◽  
Return Levels ◽  
Wave Heights ◽  
Local Extreme

<p>To estimate return levels of wave heights (Hs) induced by tropical cyclones at the coast, a commonly-used approach is to (1) randomly generate a large number of synthetic cyclone events (typically >1,000); (2) numerically simulate the corresponding Hs over the whole domain of interest; (3) extract the Hs values at the desired location at the coast and (4) perform the local extreme value analysis (EVA) to derive the corresponding return level. Step 2 is however very constraining because it often involves a numerical hydrodynamic simulator that can be prohibitive to run: this might limit the number of results to perform the local EVA (typically to several hundreds). In this communication, we propose a spatial stochastic simulation procedure to increase the database size of numerical results with synthetic maps of Hs that are stochastically generated. To do so, we propose to rely on a data-driven dimensionality-reduction method, either unsupervised (Principal Component Analysis) or supervised (Partial Least Squares Regression), that is trained with a limited number of pre-existing numerically simulated Hs maps. The procedure is applied to the Guadeloupe island and results are compared to the commonly-used approach applied to a large database of Hs values computed for nearly 2,000 synthetic cyclones (representative of 3,200 years – Krien et al., NHESS, 2015). When using only a hundred of cyclones, we show that the estimates of the 100-year return levels can be achieved with a mean absolute percentage error (derived from a bootstrap-based procedure) ranging between 5 and 15% around the coasts while keeping the width of the 95% confidence interval of the same order of magnitude than the one using the full database. Without synthetic Hs maps augmentation, the error and confidence interval width are both increased by nearly 100%. A careful attention is paid to the tuning of the approach by testing the sensitivity to the spatial domain size, the information loss due to data compression, and the number of cyclones. This study has been carried within the Carib-Coast INTERREG project (https://www.interreg-caraibes.fr/carib-coast).</p>

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