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.
Original language | English |
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Pages (from-to) | 3857-3878 |
Number of pages | 22 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 40 |
Issue number | 21 |
DOIs | |
Publication status | Published - 2011 |
Externally published | Yes |
Keywords
- Categorical covariate
- Dimension reduction
- Eigen decomposition
- Sliced Inverse Regression (SIR)