Premium
HIGH‐DIMENSIONAL PARAMETRIC MODELLING OF MULTIVARIATE EXTREME EVENTS
Author(s) -
Stephenson Alec G.
Publication year - 2009
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2008.00528.x
Subject(s) - multivariate statistics , extreme value theory , mathematics , markov chain monte carlo , parametric statistics , parametric model , generalized extreme value distribution , parametrization (atmospheric modeling) , statistics , bayesian probability , physics , quantum mechanics , radiative transfer
Summary Multivariate extreme events are typically modelled using multivariate extreme value distributions. Unfortunately, there exists no finite parametrization for the class of multivariate extreme value distributions. One common approach is to model extreme events using some flexible parametric subclass. This approach has been limited to only two or three dimensions, primarily because suitably flexible high‐dimensional parametric models have prohibitively complex density functions. We present an approach that allows a number of popular flexible models to be used in arbitrarily high dimensions. The approach easily handles missing and censored data, and can be employed when modelling componentwise maxima and multivariate threshold exceedances. The approach is based on a representation using conditionally independent marginal components, conditioning on positive stable random variables. We use Bayesian inference, where the conditioning variables are treated as auxiliary variables within Markov chain Monte Carlo simulations. We demonstrate these methods with an application to sea‐levels, using data collected at 10 sites on the east coast of England.