  In this paper we consider a semiparametric regression model involving a
$d$-dimensional quantitative explanatory variable $X$ and including a dimension
reduction of $X$ via an index $\beta'X$. In this model, the main goal is to
estimate the euclidean parameter $\beta$ and to predict the real response
variable $Y$ conditionally to $X$. Our approach is based on sliced inverse
regression (SIR) method and optimal quantization in $\mathbf{L}^p$-norm. We
obtain the convergence of the proposed estimators of $\beta$ and of the
conditional distribution. Simulation studies show the good numerical behavior
of the proposed estimators for finite sample size.
