Skip Navigation



Biometrika Advance Access published online on August 5, 2007
Biometrika, doi:10.1093/biomet/asm043
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
94/3/615    most recent
asm043v1
Right arrow References
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 Li, L.
Right arrow Articles by Tsai, C.-L.
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

Article

Partial inverse regression

Lexin Li

Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695, U.S.A.

R. Dennis Cook

School of Statistics, University of Minnesota, St Paul, Minnesota 55108, U.S.A.

Chih-Ling Tsai

Graduate School of Management, University of California, Davis, California 95616, U.S.A.

li{at}stat.ncsu.edu

dennis{at}stat.umn.edu

cltsai{at}ucdavis.edu

Received for publication 1 March 2005. Revision received 1 December 2006.
  Abstract

In regression with a vector of quantitative predictors, sufficient dimension reduction methods can effectively reduce the predictor dimension, while preserving full regression information and assuming no parametric model. However, all current reduction methods require the sample size n to be greater than the number of predictors p. It is well known that partial least squares can deal with problems with n < p. We first establish a link between partial least squares and sufficient dimension reduction. Motivated by this link, we then propose a new dimension reduction method, entitled partial inverse regression. We show that its sample estimator is consistent, and that its performance is similar to or superior to partial least squares when n < p, especially when the regression model is nonlinear or heteroscedastic. An example involving the spectroscopy analysis of biscuit dough is also given.

Key Words: Partial least squares • Single-index model • Sliced inverse regression


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




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.