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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Estimating the limiting shape of bivariate scaled sample clouds
T2 - with additional benefits of self-consistent inference for existing extremal dependence properties
AU - Simpson, Emma
AU - Tawn, Jonathan
PY - 2024/12/31
Y1 - 2024/12/31
N2 - 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 (2010) and Nolde (2014) highlight the importance of studying the limiting shape of an appropriately-scaled sample cloud when characterising the whole joint tail. We nowdevelop 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 (2022) 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.
AB - 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 (2010) and Nolde (2014) highlight the importance of studying the limiting shape of an appropriately-scaled sample cloud when characterising the whole joint tail. We nowdevelop 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 (2022) 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.
U2 - 10.1214/24-EJS2300
DO - 10.1214/24-EJS2300
M3 - Journal article
VL - 18
SP - 4582
EP - 4611
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
IS - 2
ER -