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Accounting for choice of measurement scale in extreme value modeling

Wadsworth, Jennifer and Tawn, Jon and Jonathan, Philip (2010) Accounting for choice of measurement scale in extreme value modeling. Annals of Applied Statistics, 4 (3). pp. 1558-1578. ISSN 1932-6157

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    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.

    Item Type: Article
    Journal or Publication Title: Annals of Applied Statistics
    Uncontrolled Keywords: Extreme value theory ; Box–Cox transformation ; reparameterization ; significant wave height
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 54870
    Deposited By: ep_importer_pure
    Deposited On: 06 Jun 2012 10:50
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 15:43
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/54870

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