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A moving window approach for nonparametric estimation of the conditional tail index

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  • Gardes, Laurent
  • Girard, Stéphane

Abstract

We present a nonparametric family of estimators for the tail index of a Pareto-type distribution when covariate information is available. Our estimators are based on a weighted sum of the log-spacings between some selected observations. This selection is achieved through a moving window approach on the covariate domain and a random threshold on the variable of interest. Asymptotic normality is proved under mild regularity conditions and illustrated for some weight functions. Finite sample performances are presented on a real data study.

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  • Gardes, Laurent & Girard, Stéphane, 2008. "A moving window approach for nonparametric estimation of the conditional tail index," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2368-2388, November.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:10:p:2368-2388
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    1. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2023. "A Weissman-type estimator of the conditional marginal expected shortfall," Econometrics and Statistics, Elsevier, vol. 27(C), pages 173-196.
    2. Chavez-Demoulin, Valérie & Guillou, Armelle, 2018. "Extreme quantile estimation for β-mixing time series and applications," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 59-74.
    3. Yaolan Ma & Bo Wei & Wei Huang, 2020. "A nonparametric estimator for the conditional tail index of Pareto-type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 17-44, January.
    4. Davide Ceresetti & Eugen Ursu & Julie Carreau & Sandrine Anquetin & Jean-Dominique Creutin & Laurent Gardes & Stéphane Girard & Gilles Molinie, 2012. "Evaluation of classical spatial-analysis schemes of extreme rainfall," Post-Print hal-00780197, HAL.
    5. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    6. Yuri Goegebeur & Armelle Guillou & Théo Rietsch, 2015. "Robust conditional Weibull-type estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 479-514, June.
    7. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    8. 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.
    9. Silvia Sarpietro & Yuya Sasaki & Yulong Wang, 2022. "Non-Existent Moments of Earnings Growth," Papers 2203.08014, arXiv.org, revised Feb 2024.
    10. Gardes, Laurent & Girard, Stéphane & Lekina, Alexandre, 2010. "Functional nonparametric estimation of conditional extreme quantiles," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 419-433, February.
    11. 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.
    12. Ma, Yaolan & Jiang, Yuexiang & Huang, Wei, 2018. "Empirical likelihood based inference for conditional Pareto-type tail index," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 114-121.

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