Open Access
Translator Disclaimer
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

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.

Citation

Download Citation

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. https://doi.org/10.1214/11-AOS962

Information

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

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

Subjects:
Primary: 62H20
Secondary: 62J07

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

Rights: Copyright © 2012 Institute of Mathematical Statistics

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.40 • No. 1 • February 2012
Back to Top