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On the estimation of the functional Weibull tail-coefficient

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  • Gardes, Laurent
  • Girard, Stéphane

Abstract

We present a nonparametric family of estimators for the tail index of a Weibull tail-distribution when functional covariate is available. Our estimators are based on a kernel estimator of extreme conditional quantiles. Asymptotic normality of the estimators is proved under mild regularity conditions. Their finite sample performances are illustrated both on simulated and real data.

Suggested Citation

  • Gardes, Laurent & Girard, Stéphane, 2016. "On the estimation of the functional Weibull tail-coefficient," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 29-45.
    • Handle: RePEc:eee:jmvana:v:146:y:2016:i:c:p:29-45
    DOI: 10.1016/j.jmva.2015.05.007
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    References listed on IDEAS

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    1. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    2. Jean Diebolt & Laurent Gardes & Stéphane Girard & Armelle Guillou, 2008. "Bias-reduced estimators of the Weibull tail-coefficient," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 311-331, August.
    3. Beirlant, J. & Bouquiaux, C. & Werker, B.J.M., 2006. "Semiparametric lower bounds for tail-index estimation," Other publications TiSEM 4f434455-72a7-4b68-b972-d, Tilburg University, School of Economics and Management.
    4. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    5. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Samanta, M., 1989. "Non-parametric estimation of conditional quantiles," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 407-412, April.
    7. Beirlant, Jan & Teugels, Jozef L., 1992. "Modeling large claims in non-life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 11(1), pages 17-29, April.
    8. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    9. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 311-333, August.
    10. Jonathan El Methni & Laurent Gardes & Stéphane Girard, 2014. "Non-parametric Estimation of Extreme Risk Measures from Conditional Heavy-tailed Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 988-1012, December.
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