Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):603-613; doi:10.1093/biomet/asm044
Copyright © 2007 Biometrika Trust
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Sparse sufficient dimension reduction
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.
li{at}stat.ncsu.edu
Received for publication 1 December 2005. Revision received 1 December 2006.
Existing sufficient dimension reduction methods suffer from the fact that each dimension reduction component is a linear combination of all the original predictors, so that it is difficult to interpret the resulting estimates. We propose a unified estimation strategy, which combines a regression-type formulation of sufficient dimension reduction methods and shrinkage estimation, to produce sparse and accurate solutions. The method can be applied to most existing sufficient dimension reduction methods such as sliced inverse regression, sliced average variance estimation and principal Hessian directions. We demonstrate the effectiveness of the proposed method by both simulations and real data analysis.
Key Words: Lasso • Shrinkage sparse estimator • Sufficient dimension reduction
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