Some extensions of multivariate sliced inverse regression

Abstract

Multivariate sliced inverse regression (SIR) is a method for achieving dimension reduction in regression problems when the outcome variable y and the regressor x are both assumed to be multidimensional. In this paper, we extend the existing approaches, based on the usual SIR _I which only uses the inverse regression curve, to methods using properties of the inverse conditional variance. Contrary to the existing ones, these new methods are not blind for symmetric dependencies and rely on the SIR _II or SIR_α. We also propose their corresponding pooled slicing versions. We illustrate the usefulness of these approaches on simulation studies.

Keywords:

• Complete slicing
• Marginal slicing
• Pooled marginal slicing
• Alternating SIR
• Semi-parametric regression model
• Sliced inverse regression (SIR)
• Pooled slicing

Acknowledgements

The authors are grateful to the Editor, the Associate Editor, and two anonymous referees for contributing to the improvement of this paper through many useful remarks, suggestions, and detailed comments.