EXTREMES AND PARAMETRIC APPROACHES

• This review paper focuses on statistical issues arising in modeling univariate extremes of a random sample. In the last three decades there has been a shift from the area of parametric statistics of extremes, based on probabilistic asymptotic results in ex-treme value theory, towards a semi-parametric approach, where the estimation of the right and/or left tail-weight is performed under a quite general framework. But new parametric models can still be of high interest for the analysis of extreme events, if associated with appropriate statistical inference methodologies. After a brief reference to Gumbel’s classical block methodology and later improvements in the parametric framework, we present an overview of the developments on the estimation of parame-ters of extreme events and testing of extreme value conditions under a semi-parametric framework, and discuss a few challenging open research topics. Key-Words: • extreme value index; parameters of extreme events; parametric and semi-parametric estimation and testing; statistics of univariate extremes. AMS Subject Classification