The tail of a bivariate distribution function in the domain of attraction of a bivariate extreme-value distribution may be approximated by the one of its extreme-value attractor. The extreme-value attractor has margins that belong
to a three-parameter family and a dependence structure which is characterised by a probability measure on the unit interval with mean equal to one half, called spectral measure. Inference is done in a Bayesian framework using a censored-likelihood approach. A prior distribution is constructed on an infinite-dimensional model for this measure, the model being at the same time dense and computationally manageable. A trans-dimensional Markov chain Monte Carlo algorithm is developed and convergence to the posterior distribution is established.
In a practical perspective, this is useful for computing rare event probabilities and extreme conditional quantiles.
In simulations, the Bayes estimator for the spectral measure is shown to compare favorably with frequentist nonparametric estimators. An application to a data-set of Danish fire insurance claims is provided, with special attention on convergence diagnostics.
|
2