Abstract : This habilitation thesis summarizes my research works in the three following topics: inference on Weibull tail distributions, conditional extreme quantile estimation and reduction of dimension in a regression context. As part of the first topic, we proposed several estimators of the shape parameter and of extreme quantiles of Weibull tail distribution. A theoretical study of these estimators has also been done. Second and third topics are motivated by concrete applications: rainfalls return level estimation and study of hyperspectral images respectively. In a theoretical point of view, we proposed and studied, in the second topic, conditional extreme quantile estimators. In the third topic, a regularization of the Sliced Inverse Regression (SIR) is proposed.