Optimal quantization applied to sliced inverse regression

TitleOptimal quantization applied to sliced inverse regression
Publication TypeJournal Article
Year of Publication2011
AuthorsRomain Azaïs, Anne Gégout-Petit, and Jérôme Saracco
Keywordsoptimal quantization, reduction dimension, semiparametric regression model, sliced inverse regression (SIR)

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 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 $ L^p $-norm. We obtain the convergence of the proposed estimators of and of the conditional distribution. Simulation studies show the good numerical behavior of the proposed estimators for finite sample size.