Non-asymptotic confidence sets for input-output transfer functions

In this paper we consider the problem of constructing confidence sets for the parameters of linear systems in the presence of arbitrary noise. The developed LSCR method (Leave-out Sign dominated Correlation Regions) delivers confidence regions for the model parameters with guaranteed probability. All results hold rigorously true for any finite number of data points and no asymptotic theory is involved. Moreover, prior knowledge on the uncertainty affecting the data is reduced to a minimum. The approach is illustrated on a simulation example, showing that it delivers practically useful confidence sets with guaranteed probabilities even when the noise is biased.