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On the Choice of Norms in System Identification
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1996 (English)Report (Other academic)
Abstract [en]

In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 1996. , 18 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 1832
Keyword [en]
Robustness, Statistical estimation
Keyword [sv]
Cybernetik Informationsteori, Matematisk Statistik
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55301ISRN: LiTH-ISY-R-1832OAI: oai:DiVA.org:liu-55301DiVA: diva2:315823
Available from: 2010-04-29 Created: 2010-04-29 Last updated: 2014-08-05Bibliographically approved

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Ljung, Lennart

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