Open Access
February 2012 Estimating sufficient reductions of the predictors in abundant high-dimensional regressions
R. Dennis Cook, Liliana Forzani, Adam J. Rothman
Ann. Statist. 40(1): 353-384 (February 2012). DOI: 10.1214/11-AOS962


We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are consistent in a variety of settings, particularly in abundant regressions where most predictors contribute some information on the response, and oracle rates are possible. Simulation results are presented to support the theoretical conclusion.


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R. Dennis Cook. Liliana Forzani. Adam J. Rothman. "Estimating sufficient reductions of the predictors in abundant high-dimensional regressions." Ann. Statist. 40 (1) 353 - 384, February 2012.


Published: February 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1246.62150
MathSciNet: MR3014310
Digital Object Identifier: 10.1214/11-AOS962

Primary: 62H20
Secondary: 62J07

Keywords: central subspace , oracle property , principal fitted components , Sparsity , SPICE , sufficient dimension reduction

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 1 • February 2012
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