TY - JOUR

T1 - Some benefits of standardisation for conditional extremes

AU - Rohrbeck, Christian

AU - Tawn, Jonathan

PY - 2024/1/14

Y1 - 2024/1/14

N2 - A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes many different asymptotic theories have been proposed, partly as a consequence of the lack of ordering property with vector random variables. One class of multivariate models, based on conditional limit theory as one variable becomes extreme, developed by Heffernan and Tawn (2004), has received wide practical usage. The underpinning value of this approach has been supported by further theoretical characterisations of the limiting relationships by Heffernan and Resnick (2007) and Resnick and Zeber (2014). However, Drees and Jansen (2017) provide a number of counterexamples to their results. This paper studies these counterexamples in the Keef et al. (2013) framework, which involves marginal standardisation to a common exponentially decaying tailed marginal distribution. Our calculations show that some of the issues identified by Drees and Jensen (2017) can be addressed in this way.

AB - A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes many different asymptotic theories have been proposed, partly as a consequence of the lack of ordering property with vector random variables. One class of multivariate models, based on conditional limit theory as one variable becomes extreme, developed by Heffernan and Tawn (2004), has received wide practical usage. The underpinning value of this approach has been supported by further theoretical characterisations of the limiting relationships by Heffernan and Resnick (2007) and Resnick and Zeber (2014). However, Drees and Jansen (2017) provide a number of counterexamples to their results. This paper studies these counterexamples in the Keef et al. (2013) framework, which involves marginal standardisation to a common exponentially decaying tailed marginal distribution. Our calculations show that some of the issues identified by Drees and Jensen (2017) can be addressed in this way.

U2 - 10.1002/sta4.647

DO - 10.1002/sta4.647

M3 - Journal article

VL - 13

JO - Stat

JF - Stat

SN - 2049-1573

IS - 1

M1 - e647

ER -