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 different bia...
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| Veröffentlicht in: | IEEE access 2018-01, Vol.6, p.22165-22173 |
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| creator | He, Zhangming Wang, Dayi Zhou, Haiyin Wang, Jiongqi |
| 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. |
| doi_str_mv | 10.1109/ACCESS.2018.2812762 |
| format | Article |
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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.</description><identifier>ISSN: 2169-3536</identifier><identifier>EISSN: 2169-3536</identifier><identifier>DOI: 10.1109/ACCESS.2018.2812762</identifier><identifier>CODEN: IAECCG</identifier><language>eng</language><publisher>Piscataway: IEEE</publisher><subject>Biased estimation ; Condition monitoring ; Estimation ; Fault diagnosis ; generalized contraction mapping ; generalized ridge estimation ; improved principal component estimation ; Mapping ; Mathematical model ; Matrix algebra ; Matrix methods ; Noise measurement ; Parameter estimation ; principal component estimation ; Reactive power ; Theorems</subject><ispartof>IEEE access, 2018-01, Vol.6, p.22165-22173</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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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.</description><subject>Biased estimation</subject><subject>Condition monitoring</subject><subject>Estimation</subject><subject>Fault diagnosis</subject><subject>generalized contraction mapping</subject><subject>generalized ridge estimation</subject><subject>improved principal component estimation</subject><subject>Mapping</subject><subject>Mathematical model</subject><subject>Matrix algebra</subject><subject>Matrix methods</subject><subject>Noise measurement</subject><subject>Parameter estimation</subject><subject>principal component estimation</subject><subject>Reactive power</subject><subject>Theorems</subject><issn>2169-3536</issn><issn>2169-3536</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>ESBDL</sourceid><sourceid>RIE</sourceid><sourceid>DOA</sourceid><recordid>eNpNUU1PwkAQ3RhNJMgv4NLEM7gf3a8jNIgkGA7oeTO2U7KktnVbDvrrXSgxzmVmXt57M8kjZMronDFqnxZZttrv55wyM-eGca34DRlxpuxMSKFu_833ZNJ1RxrLREjqEdns2t5_QpVsfY0QkqWHDotk1Z3R3jd1srwAcVhjjQEq_xPXrKn7APmF8Apt6-vDA7kroepwcu1j8v68esteZtvdepMttrNcSNPPmLEAFBVKBRxRFEoZpKKgErkVtqRGC8OtyQ3mhQQOVANIRK01lKCYGJPN4Fs0cHRtiH-Gb9eAdxegCQcHofd5hY5GBy0klxYxtSw1XH8Yq7CQhcJU0ej1OHi1ofk6Yde7Y3MKdXzf8VRKo42UMrLEwMpD03UBy7-rjLpzBG6IwJ0jcNcIomo6qDwi_imMoJpKIX4Bw-aA0w</recordid><startdate>20180101</startdate><enddate>20180101</enddate><creator>He, Zhangming</creator><creator>Wang, Dayi</creator><creator>Zhou, Haiyin</creator><creator>Wang, Jiongqi</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>ESBDL</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7SR</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0001-9577-2684</orcidid></search><sort><creationdate>20180101</creationdate><title>Optimal Linear Biased Estimation Based on Generalized Contraction Mapping</title><author>He, Zhangming ; Wang, Dayi ; Zhou, Haiyin ; Wang, Jiongqi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c358t-189aa0e6e56a2ee3d668e03d05e2939f08738298c8ecd5a2a07aa5ee777afa613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Biased estimation</topic><topic>Condition monitoring</topic><topic>Estimation</topic><topic>Fault diagnosis</topic><topic>generalized contraction mapping</topic><topic>generalized ridge estimation</topic><topic>improved principal component estimation</topic><topic>Mapping</topic><topic>Mathematical model</topic><topic>Matrix algebra</topic><topic>Matrix methods</topic><topic>Noise measurement</topic><topic>Parameter estimation</topic><topic>principal component estimation</topic><topic>Reactive power</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>He, Zhangming</creatorcontrib><creatorcontrib>Wang, Dayi</creatorcontrib><creatorcontrib>Zhou, Haiyin</creatorcontrib><creatorcontrib>Wang, Jiongqi</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE Open Access Journals</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Engineered Materials Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>IEEE access</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>He, Zhangming</au><au>Wang, Dayi</au><au>Zhou, Haiyin</au><au>Wang, Jiongqi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal Linear Biased Estimation Based on Generalized Contraction Mapping</atitle><jtitle>IEEE access</jtitle><stitle>Access</stitle><date>2018-01-01</date><risdate>2018</risdate><volume>6</volume><spage>22165</spage><epage>22173</epage><pages>22165-22173</pages><issn>2169-3536</issn><eissn>2169-3536</eissn><coden>IAECCG</coden><abstract>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.</abstract><cop>Piscataway</cop><pub>IEEE</pub><doi>10.1109/ACCESS.2018.2812762</doi><tpages>9</tpages><orcidid>https://orcid.org/0000-0001-9577-2684</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Biased estimation Condition monitoring Estimation Fault diagnosis generalized contraction mapping generalized ridge estimation improved principal component estimation Mapping Mathematical model Matrix algebra Matrix methods Noise measurement Parameter estimation principal component estimation Reactive power Theorems |
| title | Optimal Linear Biased Estimation Based on Generalized Contraction Mapping |
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