{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1361137044933115136.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1111/1467-9876.00406"}},{"identifier":{"@type":"URI","@value":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2F1467-9876.00406"}},{"identifier":{"@type":"URI","@value":"https://academic.oup.com/jrsssc/article-pdf/52/3/307/50005362/jrsssc_52_3_307.pdf"}}],"dc:title":[{"@value":"A Bounded Influence Regression Estimator Based on the Statistics of the Hat Matrix"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:title>Summary</jats:title><jats:p>Many geophysical regression problems require the analysis of large (more than 104 values) data sets, and, because the data may represent mixtures of concurrent natural processes with widely varying statistical properties, contamination of both response and predictor variables is common. Existing bounded influence or high breakdown point estimators frequently lack the ability to eliminate extremely influential data and/or the computational efficiency to handle large data sets. A new bounded influence estimator is proposed that combines high asymptotic efficiency for normal data, high breakdown point behaviour with contaminated data and computational simplicity for large data sets. The algorithm combines a standard M-estimator to downweight data corresponding to extreme regression residuals and removal of overly influential predictor values (leverage points) on the basis of the statistics of the hat matrix diagonal elements. For this, the exact distribution of the hat matrix diagonal elements pii for complex multivariate Gaussian predictor data is shown to be β(pii, m, N−m), where N is the number of data and m is the number of parameters. Real geophysical data from an auroral zone magnetotelluric study which exhibit severe outlier and leverage point contamination are used to illustrate the estimator’s performance. The examples also demonstrate the utility of looking at both the residual and the hat matrix distributions through quantile–quantile plots to diagnose robust regression problems.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1381137044933115137","@type":"Researcher","foaf:name":[{"@value":"Alan D. Chave"}],"jpcoar:affiliationName":[{"@value":"Woods Hole Oceanographic Institution , USA"}]},{"@id":"https://cir.nii.ac.jp/crid/1381137044933115136","@type":"Researcher","foaf:name":[{"@value":"David J. Thomson"}],"jpcoar:affiliationName":[{"@value":"Queens University , Kingston , Canada"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"00359254"},{"@type":"EISSN","@value":"14679876"}],"prism:publicationName":[{"@value":"Journal of the Royal Statistical Society Series C: Applied Statistics"}],"dc:publisher":[{"@value":"Oxford University Press (OUP)"}],"prism:publicationDate":"2003-06-24","prism:volume":"52","prism:number":"3","prism:startingPage":"307","prism:endingPage":"322"},"reviewed":"false","dc:rights":["https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model"],"url":[{"@id":"https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2F1467-9876.00406"},{"@id":"https://academic.oup.com/jrsssc/article-pdf/52/3/307/50005362/jrsssc_52_3_307.pdf"}],"createdAt":"2004-11-15","modifiedAt":"2024-12-20","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360013168773594880","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Hydrothermal and Magmatic System of a Volcanic Island Inferred From Magnetotellurics, Seismicity, Self‐potential, and Thermal Image: An Example of Miyakejima (Japan)"}]},{"@id":"https://cir.nii.ac.jp/crid/1360576118752942336","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Direct Comparison of the Tsunami‐Generated Magnetic Field With Sea Level Change for the 2009 Samoa and 2010 Chile Tsunamis"}]},{"@id":"https://cir.nii.ac.jp/crid/1360848658216677120","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Upper mantle electrical resistivity structure beneath the central Mariana subduction system"}]},{"@id":"https://cir.nii.ac.jp/crid/2050588892108510336","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Influence of geomagnetic storms on the quality of magnetotelluric impedance"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1111/1467-9876.00406"},{"@type":"CROSSREF","@value":"10.1029/2021jb022034_references_DOI_DdrrWFc8CwA1XuqYLxXOjl3j1sn"},{"@type":"CROSSREF","@value":"10.1029/2021jb022760_references_DOI_DdrrWFc8CwA1XuqYLxXOjl3j1sn"},{"@type":"CROSSREF","@value":"10.1186/s40623-022-01659-6_references_DOI_DdrrWFc8CwA1XuqYLxXOjl3j1sn"},{"@type":"CROSSREF","@value":"10.1029/2010gc003101_references_DOI_DdrrWFc8CwA1XuqYLxXOjl3j1sn"}]}