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.

scholarly journals EXTREME VALUE ANALYSIS WITHOUT THE LARGEST VALUES: WHAT CAN BE DONE?

2019 ◽  
Vol 34 (2) ◽  
pp. 200-220
Author(s):  
Jingjing Zou ◽  
Richard A. Davis ◽  
Gennady Samorodnitsky
Keyword(s):  
Order Statistics ◽  
Extreme Values ◽  
Sample Path ◽  
Estimation Procedure ◽  
Extreme Value ◽  
Hill Estimator ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Heavy Tailed ◽  
The Hill

AbstractIn this paper, we are concerned with the analysis of heavy-tailed data when a portion of the extreme values is unavailable. This research was motivated by an analysis of the degree distributions in a large social network. The degree distributions of such networks tend to have power law behavior in the tails. We focus on the Hill estimator, which plays a starring role in heavy-tailed modeling. The Hill estimator for these data exhibited a smooth and increasing “sample path” as a function of the number of upper order statistics used in constructing the estimator. This behavior became more apparent as we artificially removed more of the upper order statistics. Building on this observation we introduce a new version of the Hill estimator. It is a function of the number of the upper order statistics used in the estimation, but also depends on the number of unavailable extreme values. We establish functional convergence of the normalized Hill estimator to a Gaussian process. An estimation procedure is developed based on the limit theory to estimate the number of missing extremes and extreme value parameters including the tail index and the bias of Hill's estimator. We illustrate how this approach works in both simulations and real data examples.

On the Applicability of Extreme Value Statistics in the Prediction of Maximum Pit Depth in Heavily Corroded Non-Piggable Buried Pipelines

2010 ◽  
Author(s):  
L. Alfonso ◽  
F. Caleyo ◽  
J. M. Hallen ◽  
J. Araujo
Keyword(s):  
Mean Squared Error ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Extreme Value Analysis ◽  
Corrosion Condition ◽  
Value Analysis ◽  
Squared Error ◽  
Different Populations ◽  
Pit Depth ◽  
Selection Of

There exists a large number of works aimed at the application of Extreme Value Statistics to corrosion. However, there is a lack of studies devoted to the applicability of the Gumbel method to the prediction of maximum pitting-corrosion depth. This is especially true for works considering the typical pit densities and spatial patterns in long, underground pipelines. In the presence of spatial pit clustering, estimations could deteriorate, raising the need to increase the total inspection area in order to obtain the desired accuracy for the estimated maximum pit depth. In most practical situations, pit-depth samples collected along a pipeline belong to distinguishable groups, due to differences in corrosion environments. For example, it is quite probable that samples collected from the pipeline’s upper and lower external surfaces will differ and represent different pit populations. In that case, maximum pit-depth estimations should be made separately for these two quite different populations. Therefore, a good strategy to improve maximum pit-depth estimations is critically dependent upon a careful selection of the inspection area used for the extreme value analysis. The goal should be to obtain sampling sections that contain a pit population as homogenous as possible with regard to corrosion conditions. In this study, the aforementioned strategy is carefully tested by comparing extreme-value-oriented Monte Carlo simulations of maximum pit depth with the results of inline inspections. It was found that the variance to mean ratio, a measure of randomness, and the mean squared error of the maximum pit-depth estimations were considerably reduced, compared with the errors obtained for the entire pipeline area, when the inspection areas were selected based on corrosion-condition homogeneity.

scholarly journals Threshold Selection for POT Framework in the Extreme Vehicle Loads Analysis Based on Multiple Criteria

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Guangrun Wu ◽  
Wenliang Qiu
Keyword(s):  
Extreme Value ◽  
Entropy Method ◽  
Distribution Functions ◽  
Multiple Criteria ◽  
Extreme Value Analysis ◽  
Threshold Selection ◽  
Value Analysis ◽  
Extreme Load ◽  
Test Criteria ◽  
Vehicle Loads

Extreme value of vehicle load plays an important role in bridge design and risk assessment. Peaks over threshold (POT) is a method commonly used in extreme load estimation. The selection of thresholds for the POT method is extremely crucial, but the selected optimal threshold varies under different test criteria. Therefore, a method to select the suitable threshold is developed based on multiple criteria decision analysis (MCDA) in the paper. In MCDA, Chi-Square (χ2) test, Kolmogorov–Smirnov (K–S) test, and Root Mean Square Error (RMSE) in probability distribution functions (PDF) are employed as the test criteria and the weight of these criteria is calculated using the entropy method. Finally, vehicle loads obtained from simulation and field measurement are adopted to validate the effectiveness and feasibility of the proposed method. The results indicate that the proposed MCDA is a useful and complementary tool for threshold selection in the extreme value analysis.

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
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