Title :
Non-asymptotic confidence ellipsoids for the least squares estimate
Author :
Weyer, Erik ; Campi, M.C.
Author_Institution :
Dept. of Electr. & Electron. Eng., Melbourne Univ., Parkville, Vic., Australia
Abstract :
In this paper we consider the finite sample properties of least squares system identification, and we derive nonasymptotic confidence ellipsoids for the estimate. Unlike asymptotic theory, the obtained confidence ellipsoids 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
Keywords :
identification; least squares approximations; LSA; asymptotic theory; confidence ellipsoids; data generating mechanism; data points; least squares estimate; least squares system identification; model order; nonasymptotic confidence ellipsoids; Automation; Ellipsoids; Least squares approximation; Least squares methods; Linear systems; Random variables; Signal generators; Stability; System identification; Transfer functions;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.914211
