Sign-Perturbed Sums : A New System Identification Approach for Constructing Exact Non-Asymptotic Confidence Regions in Linear Regression Models

We propose a new system identification method, called Sign - Perturbed Sums (SPS), for constructing nonasymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments