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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 [59] in the first time only for the independent variable X for the estimation of $ \beta$ . In a second time, we quantize the variable Im8 ${(\mover \#946 ^_n,Y)}$ 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 will submitted for publication very soon.


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