We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the Bayesian information criterion or the residual information criterion.
Bibliographical noteFunding Information:
We thank the referee and editor for their useful comments. R. D. Cook’s research was supported in part by the U.S. National Science Foundation and Chih-Ling Tsai’s research was supported in part by the U.S. National Institutes of Health.
- Shrinkage estimator
- Sliced inverse regression
- Sufficient dimension reduction