Non-asymptotic confidence ellipsoids for the least squares estimate

Abstract

In this paper we consider the finite sample properties of least squares system identification, and we derive non-asymptotic confidence ellipsoids for the estimate. Unlike asymptotic theory, the obtained confidence ellipsoids are valid for a finite number of data points. The probability that the estimate belongs to a certain ellipsoid has a natural dependence on the volume of the ellipsoid, the data generating mechanism, the model order and the number of data points available.