Semi-parametric modeling of excesses above high multivariate thresholds with censored data

How to include censored data in a statistical analysis is a recurrent issue in statistics. In multivariate extremes, the dependence structure of large observations can be characterized in terms of a non parametric angular measure, while marginal excesses above asymptotically large thresholds have a parametric distribution. In this work, a flexible semi-parametric Dirichlet mixture model for angular measures is adapted to the context of censored data and missing components. One major issue is to take into account censoring intervals overlapping the extremal threshold, without knowing whether the corresponding hidden data is actually extreme. Further, the censored likelihood needed for Bayesian inference has no analytic expression. The first issue is tackled using a Poisson process model for extremes, whereas a data augmentation scheme avoids multivariate integration of the Poisson process intensity over both the censored intervals and the failure region above threshold. The implemented MCMC algorithm allows simultaneous estimation of marginal and dependence parameters, so that all sources of uncertainty other than model bias are captured by posterior credible intervals. The method is illustrated on simulated and real data.