This thesis presents a study of the extreme value theory and is focused on two subjects rarely analyzed: observations associated with covariates and dependence measures for pairs of observations.In the first part, we considered the case where the variable of interest is simultaneously recorded with a covariate which can be either fixed or random. The conditional tail index then depends on the covariate and we proposed several estimators with their asymptotic properties. Their behavior have been approved by simulations.In the second part, we were interested in multivariate extremes and more particularly in measuring the dependence between them. In a case of near asymptotic independence, we have to introduce new models in order to measure the dependence properly. In this context, we adapted a geostatistical tool, the madogram, and studied its asymptotic properties. We completed the study with simulations and real data of precipitations.
Extreme values : covariates and bivariate case