Team cqfd

Overall Objectives
Scientific Foundations
Application Domains
New Results
Contracts and Grants with Industry
Other Grants and Activities

Section: New Results

A sliced inverse regression approach for a stratified population

Participants : Marie Chavent, Jérôme Saracco.

We consider a semiparametric single index regression model involving a real dependent variable Y , a p -dimensional quantitative covariable X and a categorical predictor Z which defines a stratification of the population. This model includes a dimension reduction of X via an index X'$ \beta$ . We propose an approach based on sliced inverse regression in order to estimate the space spanned by the common dimension reduction direction $ \beta$ . We establish Im10 $\sqrt n$ -consistency of the proposed estimator and its asymptotic normality. Simulation study shows good numerical performance of the proposed estimator in homoscedastic and heteroscedastic cases. Extensions to multiple indices models, q -dimensional response variable and/or SIRIm11 ${}_\#945 $ -based methods are also discussed. The case of unbalanced subpopulations is treated. Finally a practical method to investigate if there is or not a common direction $ \beta$ is proposed. This work is in collaboration with Benoît Liquet (Biostatistic tea of INSERM) and Vanessa Kuentz (CEMAGREF Bordeaux) and is accepted for publication [16] .


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