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Article: Robust regularized singular value decomposition with application to mortality data

TitleRobust regularized singular value decomposition with application to mortality data
Authors
KeywordsCross-validation
Smoothing spline
Robustness
Principal component analysis
Gcv
Functional data analysis
Issue Date2013
Citation
Annals of Applied Statistics, 2013, v. 7, n. 3, p. 1540-1561 How to Cite?
AbstractWe develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leaveone- row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application. © Institute of Mathematical Statistics, 2013.
Persistent Identifierhttp://hdl.handle.net/10722/219713
ISSN
2015 Impact Factor: 1.432
2015 SCImago Journal Rankings: 1.533

 

DC FieldValueLanguage
dc.contributor.authorZhang, Lingsong-
dc.contributor.authorShen, Haipeng-
dc.contributor.authorHuang, Jianhua Z.-
dc.date.accessioned2015-09-23T02:57:47Z-
dc.date.available2015-09-23T02:57:47Z-
dc.date.issued2013-
dc.identifier.citationAnnals of Applied Statistics, 2013, v. 7, n. 3, p. 1540-1561-
dc.identifier.issn1932-6157-
dc.identifier.urihttp://hdl.handle.net/10722/219713-
dc.description.abstractWe develop a robust regularized singular value decomposition (RobRSVD) method for analyzing two-way functional data. The research is motivated by the application of modeling human mortality as a smooth two-way function of age group and year. The RobRSVD is formulated as a penalized loss minimization problem where a robust loss function is used to measure the reconstruction error of a low-rank matrix approximation of the data, and an appropriately defined two-way roughness penalty function is used to ensure smoothness along each of the two functional domains. By viewing the minimization problem as two conditional regularized robust regressions, we develop a fast iterative reweighted least squares algorithm to implement the method. Our implementation naturally incorporates missing values. Furthermore, our formulation allows rigorous derivation of leaveone- row/column-out cross-validation and generalized cross-validation criteria, which enable computationally efficient data-driven penalty parameter selection. The advantages of the new robust method over nonrobust ones are shown via extensive simulation studies and the mortality rate application. © Institute of Mathematical Statistics, 2013.-
dc.languageeng-
dc.relation.ispartofAnnals of Applied Statistics-
dc.subjectCross-validation-
dc.subjectSmoothing spline-
dc.subjectRobustness-
dc.subjectPrincipal component analysis-
dc.subjectGcv-
dc.subjectFunctional data analysis-
dc.titleRobust regularized singular value decomposition with application to mortality data-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1214/13-AOAS649-
dc.identifier.scopuseid_2-s2.0-84885085246-
dc.identifier.volume7-
dc.identifier.issue3-
dc.identifier.spage1540-
dc.identifier.epage1561-
dc.identifier.eissn1941-7330-

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