  We propose a new system identification method, called Sign-Perturbed Sums
(SPS), for constructing non-asymptotic 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.
