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Bernstein polynomial angular densities of multivariate extreme value distributions

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  • Hanson, Timothy E.
  • de Carvalho, Miguel
  • Chen, Yuhui

Abstract

To model the angular measure of a multivariate extreme value distribution, we develop a mean-constrained Bernstein polynomial over the (p−1)-dimensional simplex, along with a generalization that places mass on the simplex boundaries.

Suggested Citation

  • Hanson, Timothy E. & de Carvalho, Miguel & Chen, Yuhui, 2017. "Bernstein polynomial angular densities of multivariate extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 60-66.
    • Handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:60-66
    DOI: 10.1016/j.spl.2017.03.030
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    References listed on IDEAS

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    1. Guillotte, Simon & Perron, Francois & Segers, Johan, 2011. "Non-parametric Bayesian inference on bivariate extremes," LIDAM Reprints ISBA 2011011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. M.‐O. Boldi & A. C. Davison, 2007. "A mixture model for multivariate extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 217-229, April.
    3. Yanbing Zheng & Jun Zhu & Anindya Roy, 2010. "Nonparametric Bayesian inference for the spectral density function of a random field," Biometrika, Biometrika Trust, vol. 97(1), pages 238-245.
    4. M. Oguz-Alper & Y. G. Berger, 2016. "Modelling complex survey data with population level information: an empirical likelihood approach," Biometrika, Biometrika Trust, vol. 103(2), pages 447-459.
    5. Miguel de Carvalho & Anthony C. Davison, 2014. "Spectral Density Ratio Models for Multivariate Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 764-776, June.
    6. Simon Guillotte & François Perron & Johan Segers, 2011. "Non‐parametric Bayesian inference on bivariate extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 377-406, June.
    7. Geoffrey Jones & Wesley O. Johnson & Timothy E. Hanson & Ronald Christensen, 2010. "Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard," Biometrics, The International Biometric Society, vol. 66(3), pages 855-863, September.
    8. Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393, September.
    9. Sabourin, Anne & Naveau, Philippe, 2014. "Bayesian Dirichlet mixture model for multivariate extremes: A re-parametrization," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 542-567.
    10. Yuhui Chen & Timothy Hanson & Jiajia Zhang, 2014. "Accelerated hazards model based on parametric families generalized with Bernstein polynomials," Biometrics, The International Biometric Society, vol. 70(1), pages 192-201, March.
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    Cited by:

    1. Miguel de Carvalho & Manuele Leonelli & Alex Rossi, 2020. "Tracking change-points in multivariate extremes," Papers 2011.05067, arXiv.org.
    2. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2022. "Modelling multivariate extreme value distributions via Markov trees," LIDAM Discussion Papers ISBA 2022021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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