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Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination

Multidimensional unreplicated linear functional relationship model (MULFR) with single slope is considered where p-dimensional measurement errors are introduced. When the ratio of error variances is known, the parameters’ estimation can be considered as a generalization of the unreplicated linear fu...

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Main Authors: Syed Abu Bakar, Syed Abd Rahman, Yun Fah, Chang, Mohd. Rijal, Omar
Format: Article
Published: World Scientific and Engineering Academy and Society (WSEAS) 2010
Subjects:
TK Electrical engineering. Electronics Nuclear engineering
Online Access:http://eprints.utm.my/id/eprint/26257/
http://www.wseas.us/e-library/transactions/mathematics/2010/42-258.pdf
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spelling my.utm.262572018-11-30T06:24:40Z http://eprints.utm.my/id/eprint/26257/ Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination Syed Abu Bakar, Syed Abd Rahman Yun Fah, Chang Mohd. Rijal, Omar TK Electrical engineering. Electronics Nuclear engineering Multidimensional unreplicated linear functional relationship model (MULFR) with single slope is considered where p-dimensional measurement errors are introduced. When the ratio of error variances is known, the parameters’ estimation can be considered as a generalization of the unreplicated linear functional relationship model. However, investigation on unbiased property of the estimators are not strict-forward. Taylor approximation is applied to show the intercept and slope estimators are approximately unbiased. The consistency property is discussed using Fisher Information Matrix. The coefficient of determination for MULFR model and its properties are also studied. A simulation study is carried out to evaluate the proposed estimators of the intercept and slope, and the coefficient of determination. This coefficient of determination provides a useful analysis tool for many image processing applications. A numerical example for JPEG compressed image quality assessment is explained. World Scientific and Engineering Academy and Society (WSEAS) 2010 Article PeerReviewed Syed Abu Bakar, Syed Abd Rahman and Yun Fah, Chang and Mohd. Rijal, Omar (2010) Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination. WSEAS Transactions on Mathematics, 9 (5). 295 - 313. ISSN 1109-2769 http://www.wseas.us/e-library/transactions/mathematics/2010/42-258.pdf
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic TK Electrical engineering. Electronics Nuclear engineering
spellingShingle TK Electrical engineering. Electronics Nuclear engineering
Syed Abu Bakar, Syed Abd Rahman
Yun Fah, Chang
Mohd. Rijal, Omar
Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
description Multidimensional unreplicated linear functional relationship model (MULFR) with single slope is considered where p-dimensional measurement errors are introduced. When the ratio of error variances is known, the parameters’ estimation can be considered as a generalization of the unreplicated linear functional relationship model. However, investigation on unbiased property of the estimators are not strict-forward. Taylor approximation is applied to show the intercept and slope estimators are approximately unbiased. The consistency property is discussed using Fisher Information Matrix. The coefficient of determination for MULFR model and its properties are also studied. A simulation study is carried out to evaluate the proposed estimators of the intercept and slope, and the coefficient of determination. This coefficient of determination provides a useful analysis tool for many image processing applications. A numerical example for JPEG compressed image quality assessment is explained.
format Article
author Syed Abu Bakar, Syed Abd Rahman
Yun Fah, Chang
Mohd. Rijal, Omar
author_facet Syed Abu Bakar, Syed Abd Rahman
Yun Fah, Chang
Mohd. Rijal, Omar
author_sort Syed Abu Bakar, Syed Abd Rahman
title Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
title_short Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
title_full Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
title_fullStr Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
title_full_unstemmed Multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
title_sort multidimensional unreplicated linear functional relationship model with single slope and its coefficient of determination
publisher World Scientific and Engineering Academy and Society (WSEAS)
publishDate 2010
url http://eprints.utm.my/id/eprint/26257/
http://www.wseas.us/e-library/transactions/mathematics/2010/42-258.pdf
_version_ 1643647723479498752
score 13.211869

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