Section: New Results

Optimal quantization applied to Sliced Inverse Regression

Participants : Romain Azaïs, François Dufour, Anne Gégout-Petit, Jérôme Saracco.

We tackle the well known Slice Inverse Regression (SIR) method for a semiparametric regression model involving a quantitative variable $X$ and including a dimension reduction of $X$ via a parameter $\beta$. The response variable $Y$ is real. Our goal is to estimate $\beta$ and to predict the response variable conditionally to $X$. We adapt SIR method using optimal quantization [57] in the first time only for the independent variable $X$ for the estimation of $\beta$. In a second time, we quantize the variable $({\widehat{\beta }}_n,Y)$ in order to propose a discrete conditional law of $Y$ given $X=x$. We show the convergence of the estimator of $\beta$ and of the conditional law. Simulation studies show the numerical qualities of our estimates. This work is the object of a publication in Journal of Statistical Planning and Inference [15] and was presented in a national conference [23]