Estimating sufficient reductions of the predictors in abundant high-dimensional regressions

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)353-384
Number of pages32
JournalAnnals of Statistics
Volume40
Issue number1
DOIs
StatePublished - Feb 2012

Keywords

  • Central subspace
  • Oracle property
  • Principal fitted components
  • SPICE
  • Sparsity
  • Sufficient dimension reduction

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