Guaranteed characterization of exact non-asymptotic confidence regions as defined by LSCR and SPS

In parameter estimation, it is often desirable to supplement the estimates with an assessment of their quality. A new family of methods proposed by Campi et al. for this purpose is particularly attractive, as it makes it possible to obtain exact, nonasymptotic confidence regions under relatively mild assumptions on the noise distribution. A bottleneck of this approach, however, is the numerical characterization of these confidence regions. So far, it has been carried out by gridding, which provides no guarantee as to its results and is only applicable to low dimensional spaces. The aim of this paper is to show how interval analysis can contribute to removing this bottleneck.