Accounting for choice of measurement scale in extreme value modeling. (English) Zbl 1202.62066

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

Ann. Appl. Stat. 4, No. 3, 1558-1578 (2010).

Summary: 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 G. E. P. Box and D. R. Cox [J. R. Stat. Soc., Ser. B 26, 211–243 (1964; Zbl 0156.40104)] 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.

MSC:

62G32	Statistics of extreme values; tail inference
62F15	Bayesian inference
62E20	Asymptotic distribution theory in statistics
65C60	Computational problems in statistics (MSC2010)

Keywords:

extreme value theory; Box-Cox transformation; reparameterization; significant wave height

Citations:

Zbl 0156.40104

Software:

ismev

References:

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