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Article Dans Une Revue Journal of Statistical Planning and Inference Année : 2012

Optimal quantization applied to Sliced Inverse Regression

Résumé

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 $\beta'X$. 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.

Dates et versions

hal-00556420 , version 1 (16-01-2011)

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Anne Gégout-Petit, Romain Azaïs, Jerome Saracco. Optimal quantization applied to Sliced Inverse Regression. Journal of Statistical Planning and Inference, 2012, 142 (2), pp.481-492. ⟨10.1016/j.jspi.2011.08.006⟩. ⟨hal-00556420⟩
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