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

R. Dennis Cook; Liliana Forzani; Adam J. Rothman

doi:10.1214/11-AOS962

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

R. Dennis Cook, Liliana Forzani, Adam J. Rothman

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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 language	English (US)
Pages (from-to)	353-384
Number of pages	32
Journal	Annals of Statistics
Volume	40
Issue number	1
DOIs	https://doi.org/10.1214/11-AOS962
State	Published - Feb 2012

Keywords

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

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10.1214/11-AOS962

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

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Keywords

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