Robust estimation for possibly dependent observations: application to mixture and hidden Markov models

This dissertation presents a detailed investigation of the rho-estimation approach applied to dependent data. The work it contains establishes non-asymptotic deviation bounds with respect to a Hellinger-type loss in the most general context. From there, we obtain non-asymptotic oracle inequalities and robustness properties within the context of mixture models, hidden Markov models, and diffusion processes.