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Semi-parametric modeling of excesses above high multivariate thresholds with censored data

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  • Sabourin, Anne

Abstract

How to include censored data in a statistical analysis is a recurrent issue in statistics. In multivariate extremes, the dependence structure of large observations can be characterized in terms of a non parametric angular measure, while marginal excesses above asymptotically large thresholds have a parametric distribution. In this work, a flexible semi-parametric Dirichlet mixture model for angular measures is adapted to the context of censored data and missing components. One major issue is to take into account censoring intervals overlapping the extremal threshold, without knowing whether the corresponding hidden data is actually extreme. Further, the censored likelihood needed for Bayesian inference has no analytic expression. The first issue is tackled using a Poisson process model for extremes, whereas a data augmentation scheme avoids multivariate integration of the Poisson process intensity over both the censored intervals and the failure region above threshold. The implemented MCMC algorithm allows simultaneous estimation of marginal and dependence parameters, so that all sources of uncertainty other than model bias are captured by posterior credible intervals. The method is illustrated on simulated and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:136:y:2015:i:c:p:126-146
    DOI: 10.1016/j.jmva.2015.01.014
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    1. Einmahl, J.H.J. & Segers, J.J.J., 2008. "Maximum Empirical Likelihood Estimation of the Spectral Measure of an Extreme Value Distribution," Other publications TiSEM e9340b9a-fe69-4e77-8594-8, Tilburg University, School of Economics and Management.
    2. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    3. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    4. 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).
    5. repec:awi:wpaper:0417 is not listed on IDEAS
    6. 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.
    7. Einmahl, J.H.J. & Segers, J.J.J., 2009. "Maximum empirical likelihood estimation of the spectral measure of an extreme-value distribution," Other publications TiSEM ffef2e15-c4a8-471f-b730-1, Tilburg University, School of Economics and Management.
    8. Einmahl, J.H.J. & de Haan, L.F.M. & Piterbarg, V.I., 2001. "Nonparametric estimation of the spectral measure of an extreme value distribution," Other publications TiSEM c3485b9b-a0bd-456f-9baa-0, Tilburg University, School of Economics and Management.
    9. Einmahl, J.H.J. & Segers, J.J.J., 2008. "Maximum Empirical Likelihood Estimation of the Spectral Measure of an Extreme Value Distribution," Other publications TiSEM e9340b9a-fe69-4e77-8594-8, Tilburg University, School of Economics and Management.
    10. Guadalupe Gómez & M. Calle & Ramon Oller, 2004. "Frequentist and Bayesian approaches for interval-censored data," Statistical Papers, Springer, vol. 45(2), pages 139-173, April.
    11. 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.
    12. Wendelin Schnedler, 2005. "Likelihood Estimation for Censored Random Vectors," Econometric Reviews, Taylor & Francis Journals, vol. 24(2), pages 195-217.
    13. 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.
    14. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.
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