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Penalized likelihood inference in extreme value analyses

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  • Francesco Pauli
  • Stuart Coles

Abstract

Models for extreme values are usually based on detailed asymptotic argument, for which strong ergodic assumptions such as stationarity, or prescribed perturbations from stationarity, are required. In most applications of extreme value modelling such assumptions are not satisfied, but the type of departure from stationarity is either unknown or complex, making asymptotic calculations unfeasible. This has led to various approaches in which standard extreme value models are used as building blocks for conditional or local behaviour of processes, with more general statistical techniques being used at the modelling stage to handle the non-stationarity. This paper presents another approach in this direction based on penalized likelihood. There are some advantages to this particular approach: the method has a simple interpretation; computations for estimation are relatively straightforward using standard algorithms; and a simple reinterpretation of the model enables broader inferences, such as confidence intervals, to be obtained using MCMC methodology. Methodological details together with applications to both athletics and environmental data are given.

Suggested Citation

  • Francesco Pauli & Stuart Coles, 2001. "Penalized likelihood inference in extreme value analyses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 547-560.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:5:p:547-560
    DOI: 10.1080/02664760120047889
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    References listed on IDEAS

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    1. Michael E. Robinson & Jonathan A. Tawn, 1995. "Statistics for Exceptional Athletics Records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 499-511, December.
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    Cited by:

    1. Alejandro Ivan Aguirre-Salado & Carlos Arturo Aguirre-Salado & Ernesto Alvarado & Alicia Santiago-Santos & Guillermo Arturo Lancho-Romero, 2020. "On the Smoothing of the Generalized Extreme Value Distribution Parameters Using Penalized Maximum Likelihood: A Case Study on UVB Radiation Maxima in the Mexico City Metropolitan Area," Mathematics, MDPI, vol. 8(3), pages 1-17, March.
    2. Xin Zhao & Carl Scarrott & Les Oxley & Marco Reale, 2010. "Extreme value modelling for forecasting market crisis impacts," Applied Financial Economics, Taylor & Francis Journals, vol. 20(1-2), pages 63-72.
    3. Laurini, Fabrizio & Pauli, Francesco, 2009. "Smoothing sample extremes: The mixed model approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3842-3854, September.
    4. 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.
    5. 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.
    6. Tong Siu Tung Wong & Wai Keung Li, 2015. "Extreme values identification in regression using a peaks-over-threshold approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 566-576, March.

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