Guaranteed characterization of exact non-asymptotic confidence regions in nonlinear parameter estimation

Recently, a new family of methods has been proposed for characterizing accuracy in nonlinear parameter estimation by Campi et al. These methods make it possible to obtain exact, non-asymptotic confidence regions for the parameter estimates under relatively mild assumptions on the noise distribution, namely that the noise samples are independently and symmetrically distributed.The numerical characterization of an exact confidence region with this new approach is far from being trivial, however. The aim of this paper is to show how interval analysis, which has been used for a guaranteed characterization of confidence regions for the parameter vector in other contexts, can contribute.