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Computing Uncertainty Regions with Simultaneous Confidence Degree using Bootstrap
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2000 (English)In: Proceedings of the 12th IFAC Symposium on System Identification, 2000, 1133-1138 p.Conference paper, Published paper (Refereed)
Abstract [en]

We discuss the importance of constructing confidence regions of simultaneous confidence degree for certain statistics, e.g., the frequency function. In this contribution we show how bootstrap can be used to obtain reliable confidence regions of simultaneous confidence degree, independently of how many confidence regions we calculate. The procedure is illustrated by comparison with classical methods and Monte Carlo simulations. We will also provide an evaluation of the quality of the obtained confidence regions.

Place, publisher, year, edition, pages
2000. 1133-1138 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2289
Keyword [en]
Bootstrap, Identification, Modeling errors, Uncertainty, Simultaneous confidence degree
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-91208ISBN: 978-0080435459 (print)OAI: oai:DiVA.org:liu-91208DiVA: diva2:616625
Conference
12th IFAC Symposium on System Identification, Santa Barbara, CA, USA, June, 2000
Available from: 2013-04-17 Created: 2013-04-17 Last updated: 2014-12-18
In thesis
1. Variance Expressions and Model Reduction in System Identification
Open this publication in new window or tab >>Variance Expressions and Model Reduction in System Identification
2002 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Although system identification is now a mature research field, some problems remain unsolved. Examples of unsolved or partly unsolved problems are; accuracy of subspace identification algorithms, identification via model reduction, identification for control, and identification of non-linear systems. Some problems that fall into these categories are studied in this thesis.

This thesis discusses variance expressions in system identification. In particular, variance expressions for reduced models are analyzed.

The topic of model reduction via system identification has received little attention during the years. To understand how the variance of a high order model affects the reduced model, a general expression for the variance of the low order model as a function of the reduction method used is derived. This allows the analysis of all model reduction methods that can be written as a minimization criterion, where the function to be minimized is twice continuously differentiable. Many methods can be studied using this approach. However, the popular method of model reduction by balanced truncation of states does not immediately fit into this framework.

Many unsolved problems in system identification may be studied with the use of bootstrap methods. This statistical tool, used to assess accuracy in estimation problems, may be adopted to a series of problems in system identification and signal processing. The thesis presents how bootstrap can be adopted in the prediction error framework. In addition, we demonstrate how bootstrap can be applied to problems of constructing condence regions with a simultaneous confidence degree and calculating the variance of undermodeled models.

The thesis briefly discusses how set membership identification and prediction error identification can be combined into a more robust estimate. Finally, insights into how model validation can be performed in a more user informative way are also given.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2002. 192 p.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 730
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-98162 (URN)91-7373-253-2 (ISBN)
Public defence
2002-02-22, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Supervisors
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
More styles
Language
  • de-DE
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  • en-US
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  • sv-SE
  • Other locale
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Output format
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