Skip Navigation


Biometrika Advance Access originally published online on May 23, 2007
Biometrika 2007 94(3):569-584; doi:10.1093/biomet/asm038
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
94/3/569    most recent
asm038v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Cook, R. D.
Right arrow Articles by Chiaromonte, F.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Copyright © 2007 Biometrika Trust

Articles

Dimension reduction in regression without matrix inversion

R. Dennis Cook

School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.

Bing Li and Francesca Chiaromonte

Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

dennis{at}stat.umn.edu

bing{at}stat.psu.edu

chiaro{at}stat.psu.edu

Received for publication 1 January 2006. Revision received 1 November 2006.
  Abstract

Regressions in which the fixed number of predictors p exceeds the number of independent observational units n occur in a variety of scientific fields. Sufficient dimension reduction provides a promising approach to such problems, by restricting attention to d < n linear combinations of the original p predictors. However, standard methods of sufficient dimension reduction require inversion of the sample predictor covariance matrix. We propose a method for estimating the central subspace that eliminates the need for such inversion and is applicable regardless of the (n, p) relationship. Simulations show that our method compares favourably with standard large sample techniques when the latter are applicable. We illustrate our method with a genomics application.

Key Words: Central subspace • {Sigma}-envelope • Singularity of sample covariance


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 Phil Trans R Soc AHome page
K. P. Adragni and R. D. Cook
Sufficient dimension reduction and prediction in regression
Phil Trans R Soc A, November 13, 2009; 367(1906): 4385 - 4405.
[Abstract] [Full Text] [PDF]

Home page
 BiometrikaHome page
R. D. Cook and L. Forzani
Covariance reducing models: An alternative to spectral modelling of covariance matrices
Biometrika, December 1, 2008; 95(4): 799 - 812.
[Abstract] [PDF]


Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.