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hal.structure.identifierUniversité Bordeaux Segalen - Bordeaux 2
dc.contributor.authorLIQUET, Benoit
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorSARACCO, Jérôme
dc.date.accessioned2024-04-04T02:20:05Z
dc.date.available2024-04-04T02:20:05Z
dc.date.created2009
dc.date.issued2012
dc.identifier.issn0943-4062
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189463
dc.description.abstractEnSliced inverse regression (SIR) and related methods were introduced in order to reduce the dimensionality of regression problems. In general semiparametric regression framework, these methods determine linear combinations of a set of explanatory variables X related to the response variable Y, without losing information on the conditional distribution of Y given X. They are based on a "slicing step" in the population and sample versions. They are sensitive to the choice of the number H of slices, and this is particularly true for SIR-II and SAVE methods. At the moment there are no theoretical results nor practical techniques which allows the user to choose an appropriate number of slices. In this paper, we propose an approach based on the quality of the estimation of the effective dimension reduction (EDR) space: the square trace correlation between the true EDR space and its estimate can be used as goodness of estimation. We introduce a naïve bootstrap estimation of the square trace correlation criterion to allow selection of an "optimal" number of slices. Moreover, this criterion can also simultaneously select the corresponding suitable dimension K (number of the linear combination of X). From a practical point of view, the choice of these two parameters H and K is essential. We propose a 3D-graphical tool, implemented in R, which can be useful to select the suitable couple (H, K). An R package named "edrGraphicalTools" has been developed. In this article, we focus on the SIR-I, SIR-II and SAVE methods. Moreover the proposed criterion can be use to determine which method seems to be efficient to recover the EDR space, that is the structure between Y and X. We indicate how the proposed criterion can be used in practice. A simulation study is performed to illustrate the behavior of this approach and the need for selecting properly the number H of slices and the dimension K. A short real-data example is also provided.
dc.language.isoen
dc.publisherSpringer Verlag
dc.subject.enBootstrap
dc.subject.enDimension reduction
dc.subject.enSliced inverse regression (SIR)
dc.subject.enSliced average variance estimation (SAVE)
dc.subject.enSquare trace correlation
dc.title.enA graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches
dc.typeArticle de revue
dc.identifier.doi10.1007/s00180-011-0241-9
dc.subject.halMathématiques [math]/Statistiques [math.ST]
dc.subject.halStatistiques [stat]/Théorie [stat.TH]
bordeaux.journalComputational Statistics
bordeaux.page103-125
bordeaux.volume27
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00938090
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00938090v1
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