The Annals of Applied Statistics

Accounting for choice of measurement scale in extreme value modeling

J. L. Wadsworth, J. A. Tawn, and P. Jonathan

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 4, Number 3 (2010), 1558-1578.

Dates
First available in Project Euclid: 18 October 2010

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1287409386

Digital Object Identifier
doi:10.1214/10-AOAS333

Mathematical Reviews number (MathSciNet)
MR2758341

Zentralblatt MATH identifier
1202.62066

Keywords
Extreme value theory Box–Cox transformation reparameterization significant wave height

Citation

Wadsworth, J. L.; Tawn, J. A.; Jonathan, P. Accounting for choice of measurement scale in extreme value modeling. Ann. Appl. Stat. 4 (2010), no. 3, 1558--1578. doi:10.1214/10-AOAS333. https://projecteuclid.org/euclid.aoas/1287409386


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