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

• Published in: Extremes (Boston) 2008-03, Vol.11 (1), p.3-34
• Main Authors: Gomes, M. Ivette, Canto e Castro, Luísa, Fraga Alves, M. Isabel, Pestana, Dinis
• Format: Article
• Language: English
• Subjects: Bias; Civil Engineering; Economics; Environmental Management; Finance; Hydrogeology; Insurance; Management; Mathematics and Statistics; Quality Control; Random variables; Reliability; Safety and Risk; Statistical analysis; Statistics; Statistics for Business; Studies
• ISSN: 1386-1999; 1572-915X
• DOI: 10.1007/s10687-007-0048-9

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 .