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December 2010 Coordinate-independent sparse sufficient dimension reduction and variable selection
Xin Chen, Changliang Zou, R. Dennis Cook
Ann. Statist. 38(6): 3696-3723 (December 2010). DOI: 10.1214/10-AOS826


Sufficient dimension reduction (SDR) in regression, which reduces the dimension by replacing original predictors with a minimal set of their linear combinations without loss of information, is very helpful when the number of predictors is large. The standard SDR methods suffer because the estimated linear combinations usually consist of all original predictors, making it difficult to interpret. In this paper, we propose a unified method—coordinate-independent sparse estimation (CISE)—that can simultaneously achieve sparse sufficient dimension reduction and screen out irrelevant and redundant variables efficiently. CISE is subspace oriented in the sense that it incorporates a coordinate-independent penalty term with a broad series of model-based and model-free SDR approaches. This results in a Grassmann manifold optimization problem and a fast algorithm is suggested. Under mild conditions, based on manifold theories and techniques, it can be shown that CISE would perform asymptotically as well as if the true irrelevant predictors were known, which is referred to as the oracle property. Simulation studies and a real-data example demonstrate the effectiveness and efficiency of the proposed approach.


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Xin Chen. Changliang Zou. R. Dennis Cook. "Coordinate-independent sparse sufficient dimension reduction and variable selection." Ann. Statist. 38 (6) 3696 - 3723, December 2010.


Published: December 2010
First available in Project Euclid: 30 November 2010

zbMATH: 1204.62107
MathSciNet: MR2766865
Digital Object Identifier: 10.1214/10-AOS826

Primary: 62H20
Secondary: 62J07

Keywords: central subspace , CISE , Grassmann manifolds , oracle property , sufficient dimension reduction , Variable selection

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 6 • December 2010
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