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 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.
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- Marin, Jean-Michel & Robert, Christian P., 2007. "Bayesian Core: A practical approach to computational Bayesian statistics," Economics Papers from University Paris Dauphine 123456789/1906, Paris Dauphine University.
- McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
- Mendes, Beatriz Vaz de Melo & Lopes, Hedibert Freitas, 2004. "Data driven estimates for mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 583-598, October.
- Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
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