Théorie des valeurs extrêmes

Abstract

This work is intended as a contribution to the univariate statistics of extreme values and its applications to the calculation of risk. The purpose of this dissertation is to take a deep look at the statistical techniques applied to the measurement and management of extreme risks. The essential result obtained by Fisher-Tippett on the possible existence of limit distributions of the maximum of a sample, apparently gave rise to the idea that the theory of extreme values was something quite remarkable and very different from the classical theory of the central limit. Our aim contribution is the study of GPD models with interval censoring. Indeed, we have established that the pseudo-maximum likelihood estimates retain the properties of convergence and asymptotic normality. We applied the GPD models with interval censoring to compare two different therapies used in the treatment of woman breast cancer. Finally, we have built a Wald type hypothesis testing that allowes us to compare the two treatments.