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Biometrika 2005 92(1):242-247; doi:10.1093/biomet/92.1.242
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© 2005 Biometrika Trust

Miscellanea

A note on shrinkage sliced inverse regression

Liqiang Ni1, R. Dennis Cook2 and Chih-Ling Tsai3

1 Department of Statistics and Actuarial Science, University of Central Florida, Orlando, Florida 32816, U.S.A. lni{at}mail.ucf.edu, 2 School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. dennis{at}stat.umn.edu, 3 Graduate School of Management, University of California, Davis, California 95616, U.S.A. cltsai{at}ucdavis.edu

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.

Key Words: Garotte; Lasso; Shrinkage estimator; Sliced inverse regression; Sufficient dimension reduction

Received June 2004. Revised August 2004.


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