- Prof. Doutor Laurens de Haan – Erasmus University Rotterdam & CEAUL / Prof. Doutor Stéphane Girard – LJK & Inria Grenoble Rhône-Alpes, France
- FCUL (DEIO) – Campo Grande – Bloco C6 Piso 4 – Sala: 6.4.31 – 14:00h – 16:00h
- Quarta-feira, 28 de Maio de 2014
- Referência Projeto: Pest-OE/MAT/UI0006/2014
In extreme value theory there are two fundamental approaches, both widely used: the block maxima method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the block maxima method has not been studied thoroughly. The present paper aims at providing conditions under which the block maxima method can be justified.
We also provide a theoretical comparative study of the methods. The results are in general consistent with the vast literature on comparing the methods all based on data or fully parametric models.
In this paper we restrict attention to the i.i.d. case and focus on the probability weighted moment (PWM) estimators of Hosking, Wallis and Wood (1985).The results indicate that the block maxima method is a rather efficient method under usual practical conditions.
Value-at-risk, conditional tail expectation, conditional value-at-risk and conditional tail variance are classical risk measures. For instance, the value-at-risk is defined as the upper alpha-quantile of the loss distribution where alpha is the confidence level. We propose nonparametric estimators of these risk measures for extreme losses, i.e. when alpha tends to zero and in the case of heavy-tailed distributions depending on covariates. The asymptotic distribution of the estimators is established and their finite sample behavior is illustrated both on simulated data and on a real data set of daily rainfalls in the Cévennes-Vivarais region (France).
This is joint work with Jonathan El Methni (University of Geneva) and Laurent Gardes (University of Strasbourg).