Optimal quantization applied to Sliced Inverse Regression

Anne Gégout-Petit 1, 2 Romain Azais 1, 2 Jerome Saracco 1, 2
2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : 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.
Type de document :
Article dans une revue
Journal of Statistical Planning and Inference, Elsevier, 2012, 142 (2), pp.481-492. 〈10.1016/j.jspi.2011.08.006〉
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Contributeur : Anne Gégout-Petit <>
Soumis le : dimanche 16 janvier 2011 - 11:45:41
Dernière modification le : jeudi 11 janvier 2018 - 06:22:11

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

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