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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Authors: | M Ivette Gomes Luísa Canto e Castro M Isabel Fraga Alves Dinis Pestana |
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Institution: | (1) CEAUL, DEIO, Faculty of Science, University of Lisbon, Lisbon, Portugal |
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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.
To Laurens de Haan, a token of friendship. |
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Keywords: | Extreme value index Parametric and semi-parametric estimation Statistics of extremes |
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