Résumé
Sliced Inverse Regression (SIR) is a nonparametric method for achieving dimension reduction in regression problems. It is widely applicable, very easy to implement on a computer and requires no nonparametric smoothing devices such as kernel regression or smoothing splines regression. The first moment-based SIR has been extensively studied. However, one major restriction is its vulnerability to symmetric dependencies. Methods based on second moments have been suggested as a remedy, one is called SIRα. In this paper, we establish the asymptotic normality of the SIRα estimates.