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Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions

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Abstract

In the last decades there has been a shift from the parametric statistics of extremes for IID random variables, based on the probabilistic asymptotic results in extreme value theory, towards a semi-parametric approach, where the estimation of the right tail-weight, under a quite general framework, is of major importance. After a brief presentation of classical Gumbel’s block methodology and of later improvements in the parametric framework (multivariate and multi-dimensional extreme value models for largest observations and peaks over threshold approaches), we present a coordinated overview, over the last three decades, of the developments on the estimation of the extreme value index under a semiparametric framework. Laurens de Haan has been one of the leading scientists in the field, (co-)author of many seminal ideas, that he generously shared with dozens (literally) of colleagues and students, thus achieving one of the main goals in a scientist’s life: he gathered around him a bunch of colleagues united in the endeavour of building knowledge. The last section is a personal tribute to Laurens, who fully lives his ideal that co-operation is the heart of Science.

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Authors and Affiliations

  1. CEAUL, DEIO, Faculty of Science, University of Lisbon, Lisbon, Portugal

    M. Ivette Gomes, Luísa Canto e Castro, M. Isabel Fraga Alves & Dinis Pestana

Authors
  1. M. Ivette Gomes
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  2. Luísa Canto e Castro
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  3. M. Isabel Fraga Alves
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  4. Dinis Pestana
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Corresponding author

Correspondence to M. Ivette Gomes.

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To Laurens de Haan, a token of friendship.

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Gomes, M.I., Canto e Castro, L., Fraga Alves, M.I. et al. Statistics of extremes for IID data and breakthroughs in the estimation of the extreme value index: Laurens de Haan leading contributions. Extremes 11, 3–34 (2008). https://doi.org/10.1007/s10687-007-0048-9

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  • DOI: https://doi.org/10.1007/s10687-007-0048-9

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