M-estimation and Median of Means applied to statistical learning.

Summary The main objective of this thesis is to study robust statistical learning methods. Traditionally, in statistics we use models or simplifying assumptions that allow us to represent the real world and to analyze it properly. However, some deviations from the assumptions can strongly disturb the statistical analysis of a database. By robust statistics, we mean here methods that can handle both so-called abnormal data (sensor error, human error) and data of a highly variable nature. We apply this kind of technique to statistical learning, thus giving theoretical assurances of efficiency of the proposed methods as well as illustrations on simulated and real data.