A sliced inverse regression approach for a stratified population

Chavent, Marie, Kuentz, Vanessa, Liquet, Benoit and Saracco, Jerome (2011) A sliced inverse regression approach for a stratified population. Communications in Statistics-Theory and Methods, 40 21: 3857-3878. doi:10.1080/03610926.2010.501940


Author Chavent, Marie
Kuentz, Vanessa
Liquet, Benoit
Saracco, Jerome
Title A sliced inverse regression approach for a stratified population
Journal name Communications in Statistics-Theory and Methods   Check publisher's open access policy
ISSN 0361-0926
1532-415X
Publication date 2011-01
Sub-type Article (original research)
DOI 10.1080/03610926.2010.501940
Volume 40
Issue 21
Start page 3857
End page 3878
Total pages 22
Place of publication Philadelphia, PA United States
Publisher Taylor and Francis
Collection year 2012
Language eng
Formatted abstract
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.
Keyword Categorical covariate
Dimension reduction
Eigen decomposition
Sliced Inverse Regression (SIR)
Sufficient Dimension Reduction
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Fri, 13 Sep 2013, 15:56:27 EST by Kay Mackie on behalf of School of Mathematics & Physics