Optimal Linear Biased Estimation Based on Generalized Contraction Mapping
Estimation methods are generalized in this paper by the idea of “scalar-vector-matrix”. A generalized contraction mapping (GCM) framework is proposed for searching the optimal linear biased estimation. First, based on the latent model and the mean square error criterion, four d...
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doaj-0cd5735259ee4914827b896ed5d6e4602021-03-29T20:54:30ZengIEEEIEEE Access2169-35362018-01-016221652217310.1109/ACCESS.2018.28127628307053Optimal Linear Biased Estimation Based on Generalized Contraction MappingZhangming He0Dayi Wang1Haiyin Zhou2Jiongqi Wang3https://orcid.org/0000-0001-9577-2684College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, ChinaBeijing Institute of Spacecraft System Engineering, China Academy of Space Technology, Beijing, ChinaCollege of Liberal Arts and Sciences, National University of Defense Technology, Changsha, ChinaCollege of Liberal Arts and Sciences, National University of Defense Technology, Changsha, ChinaEstimation methods are generalized in this paper by the idea of “scalar-vector-matrix”. A generalized contraction mapping (GCM) framework is proposed for searching the optimal linear biased estimation. First, based on the latent model and the mean square error criterion, four different biased estimation methods are analyzed. They are the improved principal component estimation (PCE), the improved principal component estimation (IPCE), the ridge estimation (RE), and the generalized ridge estimation (GRE). A suboptimal ridge parameter for the RE is given. Four estimation performance theorems for the four methods are obtained using the traditional contraction mapping (CM) framework. The theoretical results can ease the difficulty of choosing methods for application. Second, we generalize the CM framework into the generalized contraction mapping (GCM) framework, and the optimal linear biased estimation method based GCM is given theoretically by the geometric tools of rotation, contraction, and reflection. Therefore, the GCM framework further improves the estimation performance. Finally, a numerical experiment is designed to validate the correctness of the theorems in the paper.https://ieeexplore.ieee.org/document/8307053/Biased estimationfault diagnosisgeneralized contraction mappinggeneralized ridge estimationimproved principal component estimationparameter estimation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zhangming He Dayi Wang Haiyin Zhou Jiongqi Wang |
spellingShingle |
Zhangming He Dayi Wang Haiyin Zhou Jiongqi Wang Optimal Linear Biased Estimation Based on Generalized Contraction Mapping IEEE Access Biased estimation fault diagnosis generalized contraction mapping generalized ridge estimation improved principal component estimation parameter estimation |
author_facet |
Zhangming He Dayi Wang Haiyin Zhou Jiongqi Wang |
author_sort |
Zhangming He |
title |
Optimal Linear Biased Estimation Based on Generalized Contraction Mapping |
title_short |
Optimal Linear Biased Estimation Based on Generalized Contraction Mapping |
title_full |
Optimal Linear Biased Estimation Based on Generalized Contraction Mapping |
title_fullStr |
Optimal Linear Biased Estimation Based on Generalized Contraction Mapping |
title_full_unstemmed |
Optimal Linear Biased Estimation Based on Generalized Contraction Mapping |
title_sort |
optimal linear biased estimation based on generalized contraction mapping |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2018-01-01 |
description |
Estimation methods are generalized in this paper by the idea of “scalar-vector-matrix”. A generalized contraction mapping (GCM) framework is proposed for searching the optimal linear biased estimation. First, based on the latent model and the mean square error criterion, four different biased estimation methods are analyzed. They are the improved principal component estimation (PCE), the improved principal component estimation (IPCE), the ridge estimation (RE), and the generalized ridge estimation (GRE). A suboptimal ridge parameter for the RE is given. Four estimation performance theorems for the four methods are obtained using the traditional contraction mapping (CM) framework. The theoretical results can ease the difficulty of choosing methods for application. Second, we generalize the CM framework into the generalized contraction mapping (GCM) framework, and the optimal linear biased estimation method based GCM is given theoretically by the geometric tools of rotation, contraction, and reflection. Therefore, the GCM framework further improves the estimation performance. Finally, a numerical experiment is designed to validate the correctness of the theorems in the paper. |
topic |
Biased estimation fault diagnosis generalized contraction mapping generalized ridge estimation improved principal component estimation parameter estimation |
url |
https://ieeexplore.ieee.org/document/8307053/ |
work_keys_str_mv |
AT zhangminghe optimallinearbiasedestimationbasedongeneralizedcontractionmapping AT dayiwang optimallinearbiasedestimationbasedongeneralizedcontractionmapping AT haiyinzhou optimallinearbiasedestimationbasedongeneralizedcontractionmapping AT jiongqiwang optimallinearbiasedestimationbasedongeneralizedcontractionmapping |
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1724193903102394368 |