IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v128y2017icp60-66.html
   My bibliography  Save this article

Bernstein polynomial angular densities of multivariate extreme value distributions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715217301311
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2017.03.030?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sabourin, Anne, 2015. "Semi-parametric modeling of excesses above high multivariate thresholds with censored data," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 126-146.
    2. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    3. 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.
    4. de Carvalho, Miguel & Oumow, Boris & Segers, Johan & WarchoÅ‚, MichaÅ‚, 2012. "A Euclidean likelihood estimator for bivariate tail dependence," LIDAM Discussion Papers ISBA 2012013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    6. Vettori, Sabrina & Huser, Raphael & Segers, Johan & Genton, Marc, 2017. "Bayesian Clustering and Dimension Reduction in Multivariate Extremes," LIDAM Discussion Papers ISBA 2017017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Khader Khadraoui & Pierre Ribereau, 2019. "Bayesian Inference with M-splines on Spectral Measure of Bivariate Extremes," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 765-788, September.
    8. Burda, Martin & Prokhorov, Artem, 2014. "Copula based factorization in Bayesian multivariate infinite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 200-213.
    9. Rocco Roberto Cerchiara & Francesco Acri, 2020. "Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data," Risks, MDPI, vol. 8(3), pages 1-19, July.
    10. Li, Yunzhe & Lee, Juhee & Kottas, Athanasios, 2024. "Bayesian nonparametric Erlang mixture modeling for survival analysis," Computational Statistics & Data Analysis, Elsevier, vol. 191(C).
    11. Zheng, Yanbing, 2011. "Shape restriction of the multi-dimensional Bernstein prior for density functions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 647-651, June.
    12. Rocco Roberto Cerchiara & Francesco Acri, 2016. "Aggregate Loss Distribution And Dependence: Composite Models, Copula Functions And Fast Fourier Transform For The Danish Re Insurance Data," Working Papers 201608, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    13. 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.
    14. G. Jones & W. O. Johnson & W. D. Vink & N. French, 2012. "A Framework for the Joint Modeling of Longitudinal Diagnostic Outcome Data and Latent Infection Status: Application to Investigating the Temporal Relationship between Infection and Disease," Biometrics, The International Biometric Society, vol. 68(2), pages 371-379, June.
    15. Wang, J. & Ghosh, S.K., 2012. "Shape restricted nonparametric regression with Bernstein polynomials," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2729-2741.
    16. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    17. 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.
    18. Karabatsos, George & Walker, Stephen G., 2007. "Bayesian nonparametric inference of stochastically ordered distributions, with Pólya trees and Bernstein polynomials," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 907-913, May.
    19. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    20. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2016. "Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials," LIDAM Discussion Papers ISBA 2016020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:60-66. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.