Non-asymptotic confidence ellipsoids for the least squares estimate

E. Weyer, M.C. Campi
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)  
In this paper we consider the nite sample properties of least squares system identi cation, and we derive non-asymptotic con dence ellipsoids for the estimate. Unlike asymptotic theory, the obtained con dence ellipsoids are valid for a nite 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.
doi:10.1109/cdc.2000.914211 fatcat:vq7erxg3dvhr5gxze7s4buqyvu