Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Statistical analysis of extreme values
Statistical analysis of extreme values
A Bayesian model for local smoothing in kernel density estimation
Statistics and Computing
On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density Functions
IEEE Transactions on Computers
Bayesian Core: A Practical Approach to Computational Bayesian Statistics
Bayesian Core: A Practical Approach to Computational Bayesian Statistics
A Bayesian approach to bandwidth selection for multivariate kernel density estimation
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
A simple generalisation of the Hill estimator
Computational Statistics & Data Analysis
Bayesian analysis of tail asymmetry based on a threshold extreme value model
Computational Statistics & Data Analysis
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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.