Seminarium i matematisk statistik
Fredagen 1 december, 2000


Anne-Laure FOUGERES
Departement de Genie Mathematique et Modelisation
Institut National des Sciences Appliquees
135 Avenue de Rangueil
31077 TOULOUSE Cedex 04
FRANCE

Title : Estimation of bivariate extreme value distributions.


System failures, resistance of materials and hydrological
problems such as river floods are but a few examples of areas
of applications where extreme value modelling is appropriate 
and useful. Extreme value models arise as soon as inference
for events out of the range of observations is required.
In the bivariate context, the problem can be reformulated
on the following way: supposing that a bivariate random
sample (X_1,Y_1),..., (X_n,Y_n) with unknown
distribution is available, how can we estimate the
asymptotic behaviour of the sequence of maxima
(\max_{i=1,..., n} X_i, \max_{i=1,..., n} Y_i),
after a suitable renormalization ?
Several threshold methods have been proposed
in the literature, but their small-sample behaviours
have never been compared.
The aim of this talk is to present the different
methods, to propose a new estimator, et to provide
a comparative study based on Monte Carlo simulations.