Non-Asymptotic Confidence Regions for the Least-Squares Estimate

Abstract We propose a new finite sample system identification method, called Sign-Perturbed Sums (SPS), to estimate the parameters of dynamical systems under mild statistical assump-tions. The proposed method constructs non-asymptotic confidence regions that include the least-squares (LS) estimate and are guaranteed to contain the true parameters with a user-chosen exact probability. Our method builds on ideas imported from the “Leave-out Sign-dominant Correlation Regions ” (LSCR) approach, but, unlike LSCR, also guarantees the inclusion of the LS estimate and provides confidence regions for multiple parameters with exact probabilities. This paper presents the SPS method for FIR and ARX systems together with its main theoretical properties, as well as demonstrates the approach through simple examples and experiments