IJPAM: Volume 43, No. 1 (2008)


Sandie Ferrigno$^1$, Ali Gannoun$^2$, Jérôme Saracco$^{3,4}$Institut de Mathématiques de Bordeaux, Université Bordeaux 1, UMR CNRS 5251, 351 Cours de la Libération, Talence Cedex, 33405, FRANCE
$^1$Institute of Mathematics ``Élie Cartan''
University Henri Poincaré Nancy 1
P.O. Box 239, Vandoeuvre-lès-Nancy Cedex, 54506, FRANCE
e-mail: Sandie.Ferrigno@iecn.u-nancy.fr
$^2$CNAM - Conservatoire National des Arts et Métiers
Mathématiques CEDRIC
292 Rue Saint Martin, Paris Cedex 03, 75141, FRANCE
e-mail: ali.gannoun@cnam.fr
$^3$Institut de Mathématiques de Bordeaux
Université Bordeaux 1
351 Cours de la Libération, Talence Cedex, 33405, FRANCE
e-mail: Jerome.Saracco@math.u-bordeaux1.fr
UMR CNRS 5113, Université Montesquieu - Bordeaux IV
Avenue Léon Duguit, Pessac Cedex, 33608, FRANCE

Abstract.We consider a semiparametric regression model such that the dependent variable $y$ is linked to some indices $x\prim\beta_k$ through an unknown link function. Li [25] introduced sliced inverse regression methods (SIR-I, SIR-II and SIR$_\alpha$) in order to estimate the effective dimension reduction space spanned by the vectors $\beta_k$. These methods computationally fast and simple but are influenced by the choice of slices in the estimation process. In this paper, we suggest to use versions of SIR methods based on fuzzy clusters instead of slices which can be seen as hard clusters and we exhibit the corresponding algorithm. We illustrate the sample behaviour of the fuzzy inverse regression estimators and compare them with the SIR ones on simulation study.

Received: October 13, 2007

AMS Subject Classification: 62H12, 62H30, 62G99

Key Words and Phrases: dimension reduction, fuzzy partition, sliced inverse regression

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 1