Anna MacDonald

University of Canterbury

Mixture of parametric and non-parametric models for extreme values with threshold estimation

The traditional asymptotically motivated extreme value model for the tail(s) of distributions (exceedances over high thresholds) is the Generalised Pareto distribution. Substantial uncertainty can be introduced to tail estimates due to the selection of the threshold. Typically, somewhat subjective threshold choices are made using graphical tools. Recently, various mixture type models have been proposed for the entire distribution function, simultaneously capturing the bulk of the distribution with the flexibility of the Generalised Pareto for the upper/lower tails. These mixture models either explicitly include the threshold as a parameter to be estimated, or somewhat bypass this choice by the use of smooth transition functions between bulk and tail models.

We introduce a new mixture model, based on using smoothing techniques to capture the bulk of the distribution with the inclusion of the threshold as a parameter to be estimated, using Bayesian techniques. Comparisons of the model are made using both traditional techniques and other mixture models.

The primary goal is exploring mixture models and their application for modelling high frequency physiological measurements for preterm babies. Via the estimation of suitable quantiles, we are looking to refine our understanding of "normal ranges" for the level and variability of these measurements. The proposed model is applied to blood oxygenation from preterm babies in the neonatal intensive care units at Christchurch Women's Hospital, New Zealand.