Contributions to high dimensional statistics.

Summary The purpose of this thesis is to give an account of my contributions to high dimensional statistics. The first part is devoted to the problem of matrix completion. After presenting the problem, I describe the main results obtained in the papers [Klo11, GK17, KLMS15, Klo15, KLT16, KT15, LKMS14]. The second part is devoted to the variable coefficients model . I present the main results of the non-asymptotic studies [KP13, KP15]. Finally, the third part presents the results of [KTV16] concerning the parsimonious network model and the graphon model.