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A flexible extreme value mixture model

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Author Info

  • MacDonald, A.
  • Scarrott, C.J.
  • Lee, D.
  • Darlow, B.
  • Reale, M.
  • Russell, G.
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    Abstract

    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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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 55 (2011)
    Issue (Month): 6 (June)
    Pages: 2137-2157

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    Handle: RePEc:eee:csdana:v:55:y:2011:i:6:p:2137-2157

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Extreme values Mixture model Kernel density Threshold selection;

    References

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
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    Cited by:
    1. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    2. Dadalau Diana, 2012. "Integrated Estimation Model Of The Difficulty Status Of Entreprise," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 4, pages 130-143, December.
    3. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.

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