A Horse Race between the Block Maxima Method and the Peak–over–Threshold Approach

2021 ◽  
Vol 36 (3) ◽  
Author(s):  
Axel Bücher ◽  
Chen Zhou
Keyword(s):  
Horse Race ◽  
Peak Over Threshold ◽  
Block Maxima ◽  
Threshold Approach

Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

2014 ◽  
Vol 46 (02) ◽  
pp. 478-495 ◽  
Author(s):  
Sebastian Engelke ◽  
Alexander Malinowski ◽  
Marco Oesting ◽  
Martin Schlather
Keyword(s):  
Stable Process ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Shape Functions ◽  
Peaks Over Threshold ◽  
New Methods ◽  
Convergence Results ◽  
Block Maxima ◽  
Threshold Approach ◽  
Mixed Moving Maxima

In this paper we provide the basis for new methods of inference for max-stable processes ξ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process η in the max-domain of attraction of ξ on being extremal, several convergence results for the increments of η are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events η. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.

Comparison of Traffic Conflict Indicators for Crash Estimation using Peak Over Threshold Approach

2019 ◽  
Vol 2673 (5) ◽  
pp. 493-502 ◽  
Author(s):  
Lai Zheng ◽  
Tarek Sayed
Keyword(s):  
Confidence Intervals ◽  
Signalized Intersections ◽  
Estimation Methods ◽  
Crash Data ◽  
Time To Collision ◽  
Considerable Research ◽  
Traffic Conflicts ◽  
Peak Over Threshold ◽  
Traffic Conflict ◽  
Threshold Approach

Traffic conflict techniques have drawn considerable research interest and a number of conflict indicators have been developed. Previous studies have qualitatively analyzed indicator differences from their definitions and empirically investigated their similarities based on identified traffic conflicts. This study compares conflict indicators from a validity perspective by comparing crashes estimated from conflict indicators with observed crashes. The peak over threshold (POT) approach was employed for crash estimation. Four commonly used indicators are compared: time to collision (TTC), modified time to collision (MTTC), post encroachment time (PET), and deceleration to avoid a crash (DRAC). Based on the conflict and crash data collected from three signalized intersections, POT models are developed for different thresholds in the appropriate ranges, and crash estimation methods were proposed for individual conflict indicators. The identified conflicts and estimated crashes associated with different indicators are then compared. The results show that traffic conflicts identified by the four indicators vary, with MTTC generating the most accurate crash estimates. The crash estimates from TTC and PET are also reasonable but there is a tendency of overestimation for TTC and underestimation for PET. The crash estimates of DRAC are all outside the confidence intervals of observed crashes, which is likely related to the uncertainty of vehicle braking capacity.

Statistical Inference for Max-Stable Processes by Conditioning on Extreme Events

2014 ◽  
Vol 46 (2) ◽  
pp. 478-495 ◽  
Author(s):  
Sebastian Engelke ◽  
Alexander Malinowski ◽  
Marco Oesting ◽  
Martin Schlather
Keyword(s):  
Stable Process ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Shape Functions ◽  
Peaks Over Threshold ◽  
New Methods ◽  
Convergence Results ◽  
Block Maxima ◽  
Threshold Approach ◽  
Mixed Moving Maxima

In this paper we provide the basis for new methods of inference for max-stable processes ξ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning a process η in the max-domain of attraction of ξ on being extremal, several convergence results for the increments of η are proved. In a similar way, the shape functions of mixed moving maxima (M3) processes can be extracted from suitably conditioned single events η. Connecting the two approaches, transformation formulae for processes that admit both an incremental and an M3 representation are identified.

Effects of Waves and Currents on Extreme Loads on a Jacket

2015 ◽  
Author(s):  
Kjersti Bruserud ◽  
Sverre Haver
Keyword(s):  
Wind Waves ◽  
Offshore Structures ◽  
Load Estimation ◽  
Extreme Wave ◽  
Load Model ◽  
Extreme Loads ◽  
Extreme Load ◽  
Peak Over Threshold ◽  
Waves And Currents ◽  
Threshold Approach

In lack of simultaneous data of metocean parameters such as wind, waves and currents, Norwegian design regulations presently recommend a conservative combination of metocean parameters for estimation of characteristic metocean loads on offshore structures. A simplified parametric load model for a jacket, based on waves and currents, is assumed. Several approaches to load estimation are investigated and the following are considered; different averaging length of extreme currents, the effect of peak-over-threshold approach for estimation of extreme wave and currents compared to all-sea states approach and extreme load estimation directly from a load time series. When compared to the recommended approach, all other approaches yield a reduced estimated characteristic metocean load. The results are intended be illustrative and not suitable for use in design.

Effects of Waves and Currents on Extreme Loads on a Jacket

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Kjersti Bruserud ◽  
Sverre Haver
Keyword(s):  
Wind Waves ◽  
Offshore Structures ◽  
Load Estimation ◽  
Static Loads ◽  
Extreme Loads ◽  
Extreme Load ◽  
Peak Over Threshold ◽  
Waves And Currents ◽  
Design Calculations ◽  
Threshold Approach

In lack of simultaneous data of metocean parameters such as wind, waves, and currents, Norwegian design regulations presently recommend a conservative combination of metocean parameters for estimation of characteristic metocean loads on offshore structures. A simplified parametric load model for a jacket, based on waves and currents, is assumed. Several approaches to load estimation are investigated and the following are considered: different averaging length of extreme currents, the effect of peak-over-threshold approach for estimation of extreme wave and currents compared to all-sea states approach and extreme load estimation directly from a load time series. When compared to the recommended approach, all other approaches yield a reduced estimated characteristic metocean load. The purpose of this study is to indicate the possible conservatism in the Norwegian design regulations for estimation of quasi-static loads on a jacket. The results are intended to be illustrative and not suitable for use in specific design calculations.

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