The first part of this PhD thesis deals with combinatorial inference methods forGeometric Data Analysis (GDA). We propose multidimensional tests that make no assumption on the process of generating data or distributions. We focus particularly on problems of typicality (comparison of a mean point to a reference point or comparison of a group of observations to a reference population) and on problems of homogeneity (comparison of several groups). These methods consist in using combinatorial procedures to build a reference set with respect to which we situate the data. The chosen test statistics lead to original extensions: geometric interpretation of the observed level and construction of a compatibilityzone.The second part of this thesis presents the study of absenteeism in the French Electricity and Gas Industries from 1995 to 2011 (with construction of an epidemiological cohort). GDA methods are used to identify emerging diseases and sensitive groups of agents.
