Please use this identifier to cite or link to this item: https://doi.org/10.1006/jmva.2001.1997
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dc.titleThe deepest regression method
dc.contributor.authorMukherjee, K.
dc.contributor.authorBai, Z.D.
dc.date.accessioned2014-10-28T05:15:47Z
dc.date.available2014-10-28T05:15:47Z
dc.date.issued2002
dc.identifier.citationMukherjee, K., Bai, Z.D. (2002). The deepest regression method. Journal of Multivariate Analysis 81 (1) : 138-166. ScholarBank@NUS Repository. https://doi.org/10.1006/jmva.2001.1997
dc.identifier.issn0047259X
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/105412
dc.description.abstractDeepest regression (DR) is a method for linear regression introduced by P. J. Rousseeuw and M. Hubert (1999, J. Amer. Statis. Assoc. 94, 388-402). The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with breakdown value that converges almost surely to 1/3 in any dimension. We construct an approximate algorithm for fast computation of DR in more than two dimensions. From the distribution of the regression depth we derive tests for the true unknown parameters in the linear regression model. Moreover, we construct simultaneous confidence regions based on bootstrapped estimates. We also use the maximal regression depth to construct a test for linearity versus convexity/concavity. We extend regression depth and deepest regression to more general models. We apply DR to polynomial regression and show that the deepest polynomial regression has breakdown value 1/5. Finally, DR is applied to the Michaelis-Menten model of enzyme kinetics, where it resolves a long-standing ambiguity. © 2001 Elsevier Science (USA).
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1006/jmva.2001.1997
dc.sourceScopus
dc.subjectAlgorithm
dc.subjectInterference
dc.subjectRegression depth
dc.typeArticle
dc.contributor.departmentSTATISTICS & APPLIED PROBABILITY
dc.description.doi10.1006/jmva.2001.1997
dc.description.sourcetitleJournal of Multivariate Analysis
dc.description.volume81
dc.description.issue1
dc.description.page138-166
dc.description.codenJMVAA
dc.identifier.isiut000175333500010
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