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Simulation Study of the Calibration Technique in the Extremal Index Estimation

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Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

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Abstract

Classical extreme value methods were first derived when the underlying process is assumed to be a sequence of independent and identically distributed random variables. However, when observations are taken along the time and/or the space, the independence is an unrealistic assumption. A relevant parameter that arises in this situation is the extremal index, θ, characterizing the degree of local dependence in the extremes of a stationary series. Most of the semi-parametric estimators of this parameter show a strong dependence on the threshold u n , with an increasing bias and a decreasing variance as such a threshold decreases. A procedure based on the calibration methodology is here considered as a way of controlling the bias of an estimator. Point and interval estimates for the extremal index are obtained. A simulation study has been performed to illustrate the procedure.

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Acknowledgements

Research is partially supported by CMA and National Funds through FCT—Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011 and PTDC/FEDER. We thank the referees for carefully reading the manuscript and for their constructive remarks that greatly improved this chapter.

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Authors and Affiliations

  1. CMA and Mathematics Department, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisboa, Portugal

    D. Prata Gomes & João T. Mexia

  2. CEAUL and Mathematics Department, Instituto Superior de Agronomia, Universidade Técnica de Lisboa, Lisboa, Portugal

    M. Manuela Neves

Authors
  1. D. Prata Gomes
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  2. João T. Mexia
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  3. M. Manuela Neves
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Corresponding author

Correspondence to D. Prata Gomes .

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Editors and Affiliations

  1. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    João Lita da Silva

  2. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    Frederico Caeiro

  3. , Universidade Nova de Lisboa, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica, Caparica, 2829-516, Portugal

    Isabel Natário

  4. , Universidade Nova de Lisboa,, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica 59, Caparica, 2829-516, Portugal

    Carlos A. Braumann

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Gomes, D.P., Mexia, J.T., Neves, M.M. (2013). Simulation Study of the Calibration Technique in the Extremal Index Estimation. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_40

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