Le groupe de travail Valeurs Extrêmes et Longévité a lieu deux fois par mois : une séance sur le thème de la théorie des valeurs extrêmes et une séance sur le thème de la longévité

 Vendredi à 13h45 
Université Pierre et Marie Curie
4 place Jussieu 75005 Paris (Métro Jussieu)

Valeurs extrêmes : Nathalie Akakpo, Philippe Naveau, Maud Thomas et Olivier Wintenberger
Longévité :  Nicole El Karoui, Caroline Hillairet, Sarah Kaakai et Olivier Lopez

Prochaines séances
Vendredi 29 juin - salle 16-26 113

Julien Worms (Université de Versailles Saint Quentin en Yvelines)
 Asymptotic distribution of some extreme value index estimators under random censoring, and influence of the censoring strength in the tail
The subject of the talk will be the estimation of the extreme value index when the data at hand are randomly censored from the right. This subject has attracted attention in the recent years, with applications in the survival analysis field or in some  insurance contexts where random censoring is a challenging issue. We will consider in this talk the heavy tailed framework, along with some estimators which have proved to be, in practice, more resistant to strong censoring in the tail than previous proposals in the literature. The asymptotic distribution (and sometimes representation) of these estimators will be stated, and the influence of the strength of  censoring in the tail on the performance of these estimators will be discussed, along with the particular difficulties of the proofs. 
Extensions to other contexts (light tails, competing risks setup) will also be briefly addressed.  

Pause café

Vincent Noel (ISUP)
 Modelling Old Age Mortality Rates: an Extrapolation Method based on the Mode and the Compression of Mortality

In the last century, life expectancy has increased significantly due to medical advances and changes in lifestyle. As the aged population grows, the estimation and the modelling of mortality rates at very old ages is a major challenge. Evidence supports a complex evolution of mortality driven by three components: the decrease in premature deaths, the shift of the mortality mode to ever higher ages and the increase of the mortality compression around the mode.

Current models used to project mortality rates do not allow to reflect these three components of the mortality structure. Though current models reflect the decrease in premature mortality quite well, the shift of the mode is not properly assessed and compression of mortality around the mode over time is not allowed for. We therefore propose an extrapolation method that explicitly assesses both the mode and the compression of mortality for old ages.  We show that, for the French population, these two parameters present high historical correlations for different socio-economic categories and we thus propose a formula to derive the compression from the mode for a given sub-group of the national population.

Evidence also supports a strong link between the mode and mid-age mortality rates(60-65 years) over time.  We therefore propose a method to estimate the mode of a given sub-group of the French population based on observed mid-age mortality rates. Backtesting performed on historical French data showed high accuracy for both male and female populations. Preliminary results on Japanese and Swedish populations show that the proposed methodology could be extended to other countries.

The  proposed  method  allows  the  production  of  more  consistent  life  tables  for  sub-groups  based  on  observable  data  and  could  also  be  used  to  anticipate  long-term  trends of the mortality structure based