@article {91,
	title = {Optimal quantization applied to sliced inverse regression},
	year = {2011},
	abstract = {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 $\beta{\textquoteright}X$. In this model, the main goal is to estimate the Euclidean parameter 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 $L^p$-norm. We obtain the convergence of the proposed estimators of  and of the conditional distribution. Simulation studies show the good numerical behavior of the proposed estimators for finite sample size.},
	keywords = {optimal quantization, reduction dimension, semiparametric regression model, sliced inverse regression (SIR)},
	author = {Romain Aza{\"\i}s and Anne G{\'e}gout-Petit and J{\'e}r{\^o}me Saracco}
}
