A flexible extreme value mixture model

Extreme value theory is used to derive asymptotically motivated models for unusual or rare events, e.g. the upper or lower tails of a distribution. A new flexible extreme value mixture model is proposed combining a non-parametric kernel density estimator for the bulk of the distribution with an appr...

Full description

Saved in:
Bibliographic Details
Published in:Computational statistics & data analysis 2011-06, Vol.55 (6), p.2137-2157
Main Authors: MacDonald, A., Scarrott, C.J., Lee, D., Darlow, B., Reale, M., Russell, G.
Format: Article
Language:English
Subjects:
Asymptotic properties
Density
Estimators
Exact sciences and technology
Extreme values
Extreme values Mixture model Kernel density Threshold selection
General topics
Infants
Inference
Kernel density
Kernels
Mathematics
Mixture model
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic processes
Threshold selection
Thresholds
Uncertainty
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Extreme value theory is used to derive asymptotically motivated models for unusual or rare events, e.g. the upper or lower tails of a distribution. A new flexible extreme value mixture model is proposed combining a non-parametric kernel density estimator for the bulk of the distribution with an appropriate tail model. The complex uncertainties associated with threshold choice are accounted for and new insights into the impact of threshold choice on density and quantile estimates are obtained. Bayesian inference is used to account for all uncertainties and enables inclusion of expert prior information, potentially overcoming the inherent sparsity of extremal data. A simulation study and empirical application for determining normal ranges for physiological measurements for pre-term infants is used to demonstrate the performance of the proposed mixture model. The potential of the proposed model for overcoming the lack of consistency of likelihood based kernel bandwidth estimators when faced with heavy tailed distributions is also demonstrated.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2011.01.005