Séminaire MODAL'X : Antoine Marchina (MAP5, Université de Paris)

Résumé :
In this talk, we will provide new concentration inequalities for suprema of (possibly) non-centered and unbounded empirical processes associated with independent and identically distributed random variables. In particular, we establish Fuk-Nagaev type inequalities with the optimal constant in the moderate deviation bandwidth. The proof builds on martingale methods and comparison inequalities, allowing to bound generalized quantiles as the so-called Conditional Value-at-Risk We will also explain the use of these results in statistical applications (ongoing research).