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Estimating sufficient reductions of the predictors in abundant high-dimensional regressions
R. Dennis Cook, Liliana Forzani, Adam J. Rothman · 2012-05-30 · via math.ST updates on arXiv.org

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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