Guaranteed characterization of exact confidence regions for FIR models under mild assumptions on the noise via interval analysis
SPS is one of the two methods proposed recently by Campi et al. to obtain exact, non-asymptotic confidence regions for parameter estimates under mild assumptions on the noise distribution. It does not require the measurement noise to be Gaussian (or to have any other known distribution for that matter). The numerical characterization of the resulting confidence regions is far from trivial, however, and has only be carried out so far on very low-dimensional problems via methods that could not guarantee their results and could not be extended to large-scale problems because of their intrinsic complexity. The aim of the present paper is to show how interval analysis can contribute to a guaranteed characterization of exact confidence regions in large-scale problems. The application considered is the estimation of the parameters of finite-impulse-response (FIR) models. The structure of the problem makes it possible to define a very efficient specific contractor, allowing the treatement of models with a large number of parameters, as is the rule for FIR models, and thus escaping the curse of dimensionality that often plagues interval methods.