Advances and Applications in Statistics
Volume 34, Issue 2, Pages 85 - 105
(June 2013)
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SPARSE MAVE WITH ORACLE PENALTIES
Ali Alkenani and Keming Yu
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Abstract: Existing sufficient dimension reduction methods provide us with a way to find sufficient dimensions without the need to pre-specify a model or an error distribution. These methods replace the original variables with low-dimensional linear combinations of predictors without any loss of regression information. However, these 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.
In this article, we propose to combine the shrinkage ideas of the Adaptive Lasso, SCAD and MCP with a well-known sufficient dimension reduction method, the minimum average variance estimator MAVE, to produce sparse and accurate solutions. The performance of the proposed methods is verified by both simulation and real data analysis. |
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