Guaranteed non-asymptotic confidence regions in system identification

Authors:
M. C. Campi;E. Weyer
Affiliations:
Department of Electrical Engineering and Automation, University of Brescia, Via Branze 38, 25123 Brescia, Italy;Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, VIC 3010, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2005

Citing 7
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Abstract

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 'Leave-out 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.