Inverse regression methods based on fuzzy partitions
We consider a semiparametric regression model such that the dependent variable y is linked to some indices xβk through an unknown link function. Li (1991) introduced sliced inverse regression methods (SIR-I, SIR-II and SIRα) in order to estimate the effective dimension reduction space spanned by the vectors βk. 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. AMS Subject Classification: 62H12, 62H30, 62G99.