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Local robust and asymptotically unbiased estimation of conditional Pareto-type tails

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  • Goedele Dierckx
  • Yuri Goegebeur
  • Armelle Guillou

Abstract

We introduce a non-parametric robust and asymptotically unbiased estimator for the tail index of a conditional Pareto-type response distribution in presence of random covariates. The estimator is obtained from local fits of the extended Pareto distribution to the relative excesses over a high threshold using an adjusted minimum density power divergence estimation technique. We derive the asymptotic properties of the proposed estimator under some mild regularity conditions, and also investigate its finite sample performance with a small simulation experiment. The practical applicability of the methodology is illustrated on a dataset of calcium content measurements of soil samples. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2014. "Local robust and asymptotically unbiased estimation of conditional Pareto-type tails," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 330-355, June.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:2:p:330-355
    DOI: 10.1007/s11749-013-0350-6
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    References listed on IDEAS

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    1. Huixia Judy Wang & Deyuan Li & Xuming He, 2012. "Estimation of High Conditional Quantiles for Heavy-Tailed Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1453-1464, December.
    2. Kim, Moosup & Lee, Sangyeol, 2008. "Estimation of a tail index based on minimum density power divergence," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2453-2471, November.
    3. Beirlant, Jan & Goegebeur, Yuri, 2004. "Local polynomial maximum likelihood estimation for Pareto-type distributions," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 97-118, April.
    4. 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).
    5. Dierckx, Goedele & Goegebeur, Yuri & Guillou, Armelle, 2013. "An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 70-86.
    6. 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.
    7. Wang, Hansheng & Tsai, Chih-Ling, 2009. "Tail Index Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1233-1240.
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    Cited by:

    1. Christophe Dutang & Yuri Goegebeur & Armelle Guillou, 2016. "Robust and Bias-Corrected Estimation of the Probability of Extreme Failure Sets," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 52-86, February.
    2. Goedele Dierckx & Yuri Goegebeur & Armelle Guillou, 2021. "Local Robust Estimation of Pareto-Type Tails with Random Right Censoring," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 70-108, February.
    3. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2020. "Robust nonparametric estimation of the conditional tail dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    4. 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.
    5. Christophe Dutang & Yuri Goegebeur & Armelle Guillou, 2016. "Robust and bias-corrected estimation of the probability of extreme failure sets," Post-Print hal-01616187, HAL.
    6. Peng, Liang & Yao, Qiwei, 2017. "Estimating conditional means with heavy tails," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 14-22.
    7. Peng, Liang & Yao, Qiwei, 2017. "Estimating conditional means with heavy tails," LSE Research Online Documents on Economics 73082, London School of Economics and Political Science, LSE Library.
    8. 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.

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