Non-asymptotic confidence regions for model parameters in the presence of unmodelled dynamics

This paper deals with the problem of constructing confidence regions for the parameters of truncated series expansion models. The models are represented using orthonormal basis functions, and we extend the ‘Leave-out Sign-dominant Correlation Regions’ (LSCR) algorithm such that non-asymptotic confidence regions for the parameters can be constructed in the presence of unmodelled dynamics. The constructed regions have guaranteed probability of containing the true parameters for any finite number of data points. The algorithm is first developed for FIR models and then extended to models with generalized orthonormal basis functions. The usefulness of the developed approach is demonstrated for FIR and Laguerre models in simulation examples.