A sliced inverse regression approach for a stratified population

Marie Chavent, Vanessa Kuentz, Benoît Liquet, Jérôme Saracco*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this article, 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'β. We propose an approach based on sliced inverse regression in order to estimate the space spanned by the common dimension reduction direction β. We establish √ 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 SIRα-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 β is proposed.

Original languageEnglish
Pages (from-to)3857-3878
Number of pages22
JournalCommunications in Statistics - Theory and Methods
Issue number21
Publication statusPublished - 2011
Externally publishedYes


  • Categorical covariate
  • Dimension reduction
  • Eigen decomposition
  • Sliced Inverse Regression (SIR)


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