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Asymptotic Normality of Prediction Error Estimators for Approximate System Models
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Harvard University, Cambridge, MA, USA.
1980 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, Vol. 3, no 1-4, 29-46 p.Article in journal (Refereed) Published
Abstract [en]

A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results, are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and stationarity is not required

Place, publisher, year, edition, pages
Taylor & Francis, 1980. Vol. 3, no 1-4, 29-46 p.
Keyword [en]
Parameter estimation, Maximum likelihood, System identification
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-102123DOI: 10.1080/17442507908833135OAI: diva2:668554
Available from: 2013-12-01 Created: 2013-12-01 Last updated: 2014-02-21

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Ljung, Lennart
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Automatic ControlThe Institute of Technology
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