Modelling and inference for the body and tail regions of multivariate data

When an accurate representation of multivariate data is required across both the body (described by non-extreme observations) and the tail (defined by the extreme observations) regions, it is crucial to have a model that is able to characterise the joint behaviour across both regions. In this work, we propose dependence models that represent the entire distribution without the need to explicitly define each region. We do so by constructing copulas that are based on mixture distributions defined on the full support of the data. For such models, we derive (sub)-asymptotic dependence properties for specific model configurations, and show that they are flexible in capturing a broad range of extremal dependence structures through simulation studies.
 
Motivated by the computational resources required to evaluate the likelihood function of the proposed models, we also explore likelihood-free approaches that use neural networks to perform inference. In particular, we assess the performance of neural Bayes estimators in estimating the model parameters, both for one of the models introduced for the joint body and tail, and further complex extremal dependence models. We also propose using neural networks as classifiers for model selection. In this way, we provide a toolbox for simple fitting and model selection of complex extremal dependence models.
 

Dr Lídia André

Contact Lexy Sorrell for South West Local Group