Strong consistency of the Sign-Perturbed Sums method

Abstract

Sign-Perturbed Sums (SPS) is a recently developed non-asymptotic system identification algorithm that constructs confidence regions for parameters of dynamical systems. It works under mild statistical assumptions, such as symmetric and independent noise terms. The SPS confidence region includes the least-squares estimate, and, for any finite sample and user-chosen confidence probability, the constructed region contains the true system parameter with exactly the given probability. The main contribution in this paper is to prove that SPS is strongly consistent, in case of linear regression based models, in the sense that any false parameter will almost surely be excluded from the confidence region as the sample size tends to infinity. The asymptotic behavior of the confidence regions constructed by SPS is also illustrated by numerical experiments.