Mathematics – Statistics Theory
Scientific paper
2009-11-17
Mathematics
Statistics Theory
24 pages, 9 figures
Scientific paper
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 spectral measure, that is a probability measure on the unit interval with mean equal to one half. As an alternative to parametric modelling of the spectral measure, we propose an infinite-dimensional model which is at the same time manageable and still dense within the class of spectral measures. Inference is done in a Bayesian framework, using the censored-likelihood approach. In particular, we construct a prior distribution on the class of spectral measures and develop a trans-dimensional Markov chain Monte Carlo algorithm for numerical computations. The method provides a bivariate predictive density which can be used for predicting the extreme outcomes of the bivariate distribution. In a practical perspective, this is useful for computing rare event probabilities and extreme conditional quantiles. The methodology is validated by simulations and applied to a data-set of Danish fire insurance claims.
Guillotte Simon
Perron Francois
Segers Johan
No associations
LandOfFree
Nonparametric Bayesian Inference on Bivariate Extremes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonparametric Bayesian Inference on Bivariate Extremes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonparametric Bayesian Inference on Bivariate Extremes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-650553