  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.
