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

TL;DR

This paper develops a semi-parametric Bayesian approach using a Dirichlet mixture model to analyze multivariate extreme values with censored data, addressing challenges in likelihood computation and dependence structure estimation.

Contribution

It introduces a novel semi-parametric model for censored multivariate extremes, incorporating a data augmentation scheme and MCMC for joint inference of marginals and dependence.

Findings

Effective in handling censored and missing data in extremes

Provides credible intervals capturing uncertainty beyond model bias

Demonstrated on simulated and real datasets

Abstract

How to include censored data in a statistical analysis is a recur-rent 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 mix-ture 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 correspond-ing 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 cap-tured by posterior credible intervals. The method is illustrated on simulated and real data.