Optimal quantization applied to Sliced Inverse Regression

Details Optimal quantization applied to Sliced Inverse Regression Optimal quantization applied to Sliced Inverse Regression

2011-01-11

arxiv.org/abs/1101.2121v2

Mathematics

Statistics Theory

Scientific paper

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.

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