Bagging Versions of Sliced Inverse Regression

Abstract

Sliced Inverse Regression (SIR) introduced by Li (1991) is a well-known dimension reduction method in semiparametric regression. In this article, we propose bagging versions of SIR which consist in using bootstrap replications of the data set and in aggregating the corresponding estimators. We give the asymptotic distribution of the Bagging-SIR estimator. A simulation study is used to compare the numerical performance of the proposed alternative bagging versions of SIR with the classical SIR approach. The benefits of these methods are significant for noisy models and when the sample size is small. The R codes are available from the authors.

Keywords:

• Bootstrap
• Bagging
• Effective dimension reduction (edr) space
• Sliced inverse regression (SIR)

Mathematics Subject Classification:

• 62J02
• 62F40

Acknowledgment

The authors are very grateful to the Editor and referee for their valuable comments and constructive suggestions.