Brief Non-asymptotic confidence ellipsoids for the least-squares estimate

Authors:
Erik Weyer;M. C. Campi
Affiliations:
Department of Electrical and Electronic Engineering, University of Melbourne, Parkville, VIC. 3010, Australia;Department of Electrical Engineering and Automation, University of Brescia, Via Branze 38, 25123 Brescia, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2002

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Abstract

In this paper, we consider the finite sample properties of least-squares system identification, and derive non-asymptotic confidence ellipsoids for the estimate. The shape of the confidence ellipsoids is similar to the shape of the ellipsoids derived using asymptotic theory, but unlike asymptotic theory, they 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.