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A flexible extreme value mixture model


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


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.

Suggested Citation

  • MacDonald, A. & Scarrott, C.J. & Lee, D. & Darlow, B. & Reale, M. & Russell, G., 2011. "A flexible extreme value mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2137-2157, June.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:6:p:2137-2157

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. repec:dau:papers:123456789/1906 is not listed on IDEAS
    4. 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.
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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. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2014. "Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3489-3514, September.
    3. repec:eee:csdana:v:56:y:2012:i:12:p:4081-4096 is not listed on IDEAS
    4. 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.
    5. 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.
    6. Sigauke, Caston & Bere, Alphonce, 2017. "Modelling non-stationary time series using a peaks over threshold distribution with time varying covariates and threshold: An application to peak electricity demand," Energy, Elsevier, vol. 119(C), pages 152-166.
    7. repec:bla:jorssc:v:66:y:2017:i:1:p:93-120 is not listed on IDEAS
    8. Fernando Ferraz Nascimento & Dani Gamerman & Hedibert Freitas Lopes, 2016. "Time-varying extreme pattern with dynamic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 131-149, March.
    9. Lee, J. & Fan, Y. & Sisson, S.A., 2015. "Bayesian threshold selection for extremal models using measures of surprise," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 84-99.
    10. Sigauke, Caston & Verster, Andréhette & Chikobvu, Delson, 2013. "Extreme daily increases in peak electricity demand: Tail-quantile estimation," Energy Policy, Elsevier, vol. 53(C), pages 90-96.
    11. Cristiano Villa, 2017. "Bayesian estimation of the threshold of a generalised pareto distribution for heavy-tailed observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 95-118, March.


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