Simpson, Emma S;
Tawn, Jonathan A;
(2024)
Estimating the limiting shape of bivariate scaled sample clouds: With additional benefits of self-consistent inference for existing extremal dependence properties.
Electronic Journal of Statistics
, 18
(2)
pp. 4582-4611.
10.1214/24-EJS2300.
Preview |
Text
Simpson_24-EJS2300.pdf Download (1MB) | Preview |
Abstract
The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to model separate aspects of tail dependence, based on different asymptotic limits. Results from Balkema and Nolde [1] and Nolde [31] highlight the importance of studying the limiting shape of an appropriately-scaled sample cloud when characterising the whole joint tail. We now develop the first statistical inference for this limit set, which has considerable practical importance for a unified inference framework across different aspects of the joint tail. Moreover, Nolde and Wadsworth [32] link this limit set to various existing extremal dependence frameworks. Hence, a by-product of our new limit set inference is the first set of self-consistent estimators for several extremal dependence measures, avoiding the current possibility of contradictory conclusions. In simulations, our limit set estimator is successful across a range of distributions, and the corresponding extremal dependence estimators provide a major joint improvement and small marginal improvements over existing techniques. We consider an application to sea wave heights, where our estimates successfully capture the expected weakening extremal dependence as the distance between locations increases.
| Type: | Article |
|---|---|
| Title: | Estimating the limiting shape of bivariate scaled sample clouds: With additional benefits of self-consistent inference for existing extremal dependence properties |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/24-EJS2300 |
| Publisher version: | https://doi.org/10.1214/24-EJS2300 |
| Language: | English |
| Additional information: | This is an Open Access article published under a Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). |
| Keywords: | Bivariate extremes, coefficient of asymptotic independence, Conditional extremes, extremal dependence structure, gauge function |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10198042 |
Loading...
Loading...Loading...Loading...Archive Staff Only
 |
View Item |
