Séminaires doctorants 5 13 septembre 2006

We consider a minimum-entropy criterion to tackle some statistical signal and image processing problems. We focus on semiparametric models, with the aim to estimate a vector of unknown parameters, say θ⋆, of a given model in the presence of errors of unknown density. The lack of information on these errors is such that it is difficult to obtain both asymptotically efficient and robust procedures. We focus on an approach that consists in minimizing (an estimate of) the Shannon entropy of the residuals. The properties of entropy lead to consistent and robust semiparametric estimators, even though the density of the errors is unknown, and make it an appropriate criterion for dealing with signal and image processing problems.