A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches

Abstract : Sliced 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.
Type de document :
Article dans une revue
Computational Statistics, Springer Verlag, 2012, 27 (1), pp.103-125. 〈10.1007/s00180-011-0241-9〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00938090
Contributeur : Martine Courbin-Coulaud <>
Soumis le : mercredi 29 janvier 2014 - 10:19:50
Dernière modification le : jeudi 11 janvier 2018 - 06:22:11

Lien texte intégral

Identifiants

Collections

Citation

Benoit Liquet, Jérôme Saracco. A graphical tool for selecting the number of slices and the dimension of the model in SIR and SAVE approaches. Computational Statistics, Springer Verlag, 2012, 27 (1), pp.103-125. 〈10.1007/s00180-011-0241-9〉. 〈hal-00938090〉

Partager

Métriques

Consultations de la notice

201