Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation

Hong Wang-Jian; Tang De-zhi

doi:doi:10.11648/j.awcn.20170306.11

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Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation

Hong Wang-Jian, Tang De-zhi

Published in Advances in Wireless Communications and Networks (Volume 3, Issue 6)

Received: 5 October 2017 Accepted: 17 November 2017 Published: 5 December 2017

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Abstract

In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.

Published in	Advances in Wireless Communications and Networks (Volume 3, Issue 6)
DOI	10.11648/j.awcn.20170306.11
Page(s)	75-83
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Closed Loop Identification, Model Structure Validation, Asymptotic Region, Non-asymptotic Region

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APA Style

Hong Wang-Jian, Tang De-zhi. (2017). Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Advances in Wireless Communications and Networks, 3(6), 75-83. https://doi.org/10.11648/j.awcn.20170306.11

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ACS Style

Hong Wang-Jian; Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv. Wirel. Commun. Netw. 2017, 3(6), 75-83. doi: 10.11648/j.awcn.20170306.11

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AMA Style

Hong Wang-Jian, Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv Wirel Commun Netw. 2017;3(6):75-83. doi: 10.11648/j.awcn.20170306.11

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@article{10.11648/j.awcn.20170306.11,
  author = {Hong Wang-Jian and Tang De-zhi},
  title = {Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation},
  journal = {Advances in Wireless Communications and Networks},
  volume = {3},
  number = {6},
  pages = {75-83},
  doi = {10.11648/j.awcn.20170306.11},
  url = {https://doi.org/10.11648/j.awcn.20170306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.awcn.20170306.11},
  abstract = {In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.},
 year = {2017}
}

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TY  - JOUR
T1  - Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation
AU  - Hong Wang-Jian
AU  - Tang De-zhi
Y1  - 2017/12/05
PY  - 2017
N1  - https://doi.org/10.11648/j.awcn.20170306.11
DO  - 10.11648/j.awcn.20170306.11
T2  - Advances in Wireless Communications and Networks
JF  - Advances in Wireless Communications and Networks
JO  - Advances in Wireless Communications and Networks
SP  - 75
EP  - 83
PB  - Science Publishing Group
SN  - 2575-596X
UR  - https://doi.org/10.11648/j.awcn.20170306.11
AB  - In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.
VL  - 3
IS  - 6
ER  -

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Author Information

Hong Wang-Jian

School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China
Tang De-zhi

School of Electrical and Information Engineering, Anhui University of Technology, Ma-an-shan, China

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APA Style

Hong Wang-Jian, Tang De-zhi. (2017). Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Advances in Wireless Communications and Networks, 3(6), 75-83. https://doi.org/10.11648/j.awcn.20170306.11

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ACS Style

Hong Wang-Jian; Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv. Wirel. Commun. Netw. 2017, 3(6), 75-83. doi: 10.11648/j.awcn.20170306.11

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AMA Style

Hong Wang-Jian, Tang De-zhi. Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation. Adv Wirel Commun Netw. 2017;3(6):75-83. doi: 10.11648/j.awcn.20170306.11

Copy | Download

@article{10.11648/j.awcn.20170306.11,
  author = {Hong Wang-Jian and Tang De-zhi},
  title = {Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation},
  journal = {Advances in Wireless Communications and Networks},
  volume = {3},
  number = {6},
  pages = {75-83},
  doi = {10.11648/j.awcn.20170306.11},
  url = {https://doi.org/10.11648/j.awcn.20170306.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.awcn.20170306.11},
  abstract = {In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Asymptotic and Non-asymptotic Confidence Regions in Closed Loop Model Validation
AU  - Hong Wang-Jian
AU  - Tang De-zhi
Y1  - 2017/12/05
PY  - 2017
N1  - https://doi.org/10.11648/j.awcn.20170306.11
DO  - 10.11648/j.awcn.20170306.11
T2  - Advances in Wireless Communications and Networks
JF  - Advances in Wireless Communications and Networks
JO  - Advances in Wireless Communications and Networks
SP  - 75
EP  - 83
PB  - Science Publishing Group
SN  - 2575-596X
UR  - https://doi.org/10.11648/j.awcn.20170306.11
AB  - In this paper one way is proposed to construct asymptotic and non-asymptotic confidence regions in the problem of closed loop model validation deeply. These two asymptotic and non-asymptotic confidence regions correspond to the infinite and finite data points. Firstly one asymptotic confidence region is derived from some statistical properties on noise. The uncertainties bound of the model parameter is constructed in the probability sense by using the inner product form of the asymptotic covariance matrix, then a new technique for estimating bias and variance contributions to the model error is suggested. Secondly we modify sign perturbed sums (SPS) method to construct non-asymptotic confidence regions under a finite number of data points, where some modifications are studied for closed loop system. Finally the simulation example results confirm the identification theoretical results.
VL  - 3
IS  - 6
ER  -

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