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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 - Accounting for choice of measurement scale in extreme value modeling
AU - Wadsworth, Jennifer
AU - Tawn, Jon
AU - Jonathan, Philip
PY - 2010
Y1 - 2010
N2 - We investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. We propose the use of a Box–Cox power transformation incorporated as part of the inference procedure to account parametrically for the uncertainty surrounding the scale of extrapolation. This has the additional feature of increasing the rate of convergence of the distribution tails to an extreme value form in certain cases and thus reducing bias in the model estimation. Inference without reparameterization is practicably infeasible, so we explore a reparameterization which exploits the asymptotic theory of normalizing constants required for nondegenerate limit distributions. Inference is carried out in a Bayesian setting, an advantage of this being the availability of posterior predictive return levels. The methodology is illustrated on both simulated data and significant wave height data from the North Sea.
AB - We investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. We propose the use of a Box–Cox power transformation incorporated as part of the inference procedure to account parametrically for the uncertainty surrounding the scale of extrapolation. This has the additional feature of increasing the rate of convergence of the distribution tails to an extreme value form in certain cases and thus reducing bias in the model estimation. Inference without reparameterization is practicably infeasible, so we explore a reparameterization which exploits the asymptotic theory of normalizing constants required for nondegenerate limit distributions. Inference is carried out in a Bayesian setting, an advantage of this being the availability of posterior predictive return levels. The methodology is illustrated on both simulated data and significant wave height data from the North Sea.
KW - Extreme value theory
KW - Box–Cox transformation
KW - reparameterization
KW - significant wave height
U2 - 10.1214/10-AOAS333
DO - 10.1214/10-AOAS333
M3 - Journal article
VL - 4
SP - 1558
EP - 1578
JO - Annals of Applied Statistics
JF - Annals of Applied Statistics
SN - 1932-6157
IS - 3
ER -