|Ponente: ||Emilien Joly |
|Lugar: ||Salón Diego Bricio Hernández|
|Hora: ||1:00 pm|
|Resumen: ||In this talk, I will present a new insight into robust estimation with nonasymptotic guaranties. The interest for robust estimators goes back to the seminal work of P.J. Huber in the early seventies. Recently, it has known new important developments. The major breakthrough lies in the concentration properties that those new robust estimators have. Surprisingly, it is almost always possible to build an estimator that performs as well as in the convenient Gaussian context. In a nutshell, it fills the gap between small size confidence intervals only asymptotically valid and the pessimistic (in size) confidence intervals that hold in the finite horizon context.
I will start by giving the core ideas of the proofs of such strong concentration properties that use fairly simple probability tools. In a second part of the talk, we will discuss about the statistical applications of those tools such as Classification by the algorithm of k-means, Regression, U-statistics estimation (including small dependence), Sub-sampling concentration and Estimation in high dimension. Throughout the talk, I will mention a few open questions that may touch many different parts of Statistics, Probabilities or Computer science. Particularly, some computational challenges remain before applying those tools to very concrete data samples.|