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Local likelihood smoothing of sample extremes

Author

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  • A. C. Davison
  • N. I. Ramesh

Abstract

Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing sample extremes, based on local polynomial fitting of the generalized extreme value distribution and related models. The uncertainty of fits is assessed by using resampling methods. The methods are applied to data on extreme temperatures and on record times for the women's 3000 m race.

Suggested Citation

  • A. C. Davison & N. I. Ramesh, 2000. "Local likelihood smoothing of sample extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 191-208.
    • Handle: RePEc:bla:jorssb:v:62:y:2000:i:1:p:191-208
    DOI: 10.1111/1467-9868.00228
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    Cited by:

    1. 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.
    2. Adam Butler & Janet E. Heffernan & Jonathan A. Tawn & Roger A. Flather, 2007. "Trend estimation in extremes of synthetic North Sea surges," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(4), pages 395-414, August.
    3. 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.
    4. He, Fengyang & Cheng, Yebin & Tong, Tiejun, 2016. "Estimation of extreme conditional quantiles through an extrapolation of intermediate regression quantiles," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 30-37.
    5. M. Ghil & Pascal Yiou & Stéphane Hallegatte & B. D. Malamud & P. Naveau & A. Soloviev & P. Friederichs & V. Keilis-Borok & D. Kondrashov & V. Kossobokov & O. Mestre & C. Nicolis & H. W. Rust & P. Sheb, 2011. "Extreme events: dynamics, statistics and prediction," Post-Print hal-00716514, HAL.
    6. 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).
    7. 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.
    8. 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.
    9. Ying Hung & Li‐Hsiang Lin & C. F. Jeff Wu, 2022. "Varying coefficient frailty models with applications in single molecular experiments," Biometrics, The International Biometric Society, vol. 78(2), pages 474-486, June.
    10. 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.
    11. 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.
    12. Zhang, Qingzhao & Li, Deyuan & Wang, Hansheng, 2013. "A note on tail dependence regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 163-172.
    13. 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.
    14. Eduardo F. L. de Melo & Beatriz Vaz de Melo Mendes, 2009. "Local Estimation of Copula Based Value-at-Risk," Brazilian Review of Finance, Brazilian Society of Finance, vol. 7(1), pages 29-50.
    15. Emma F. Eastoe & Jonathan A. Tawn, 2009. "Modelling non‐stationary extremes with application to surface level ozone," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 25-45, February.
    16. Bousebata, Meryem & Enjolras, Geoffroy & Girard, Stéphane, 2023. "Extreme partial least-squares," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    17. Ferreira, H. & Scotto, M., 2002. "On the asymptotic location of high values of a stationary sequence," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 475-482, December.
    18. M. de Carvalho & K. F. Turkman & A. Rua, 2013. "Dynamic threshold modelling and the US business cycle," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 62(4), pages 535-550, August.
    19. Chiara Bocci & Enrica Caporali & Alessandra Petrucci, 2013. "Geoadditive modeling for extreme rainfall data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(2), pages 181-193, April.
    20. Claeskens, Gerda & Aerts, Marc, 2000. "On local estimating equations in additive multiparameter models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 139-148, August.
    21. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    22. Padoan, S.A. & Wand, M.P., 2008. "Mixed model-based additive models for sample extremes," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2850-2858, December.

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