Guaranteed non-asymptotic confidence regions in system identification.

In this paper we consider the problem of constructing confidence regions for the parameters
of identified models of dynamical systems. Taking a major departure from
the previous literature on the subject, we introduce a new approach called ‘Leaveout
Sign-dominant Correlation Regions’ (LSCR) which delivers confidence regions
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 noise affecting the data is reduced to a minimum. The approach is illustrated on
several simulation examples, showing that it delivers practically useful confidence
sets with guaranteed probabilities.