Résumé
Lack of objective basis for ordering multivariate observations is a major problem in extending the notion of quantiles in a multidimensional setting. Conditional quantiles are required in various biomedical or industrial problems. Numerous alternative definitions of (conditional) quantile for multidimensional variables, have been proposed in statistical literature. In this article, we focus on the notion of geometric quantile and conditional geometric quantile, based on the minimization of a loss function.