Statistical Science

Fisher Lecture: Dimension Reduction in Regression

R. Dennis Cook

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Abstract

Beginning with a discussion of R. A. Fisher’s early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with descriptions of general approaches to model-based and model-free dimension reduction in regression. It is argued that the role for principal components and related methodology may be broader than previously seen and that the common practice of conditioning on observed values of the predictors may unnecessarily limit the choice of regression methodology.

Article information

Source
Statist. Sci. Volume 22, Number 1 (2007), 1-26.

Dates
First available in Project Euclid: 1 August 2007

Permanent link to this document
http://projecteuclid.org/euclid.ss/1185975631

Digital Object Identifier
doi:10.1214/088342306000000682

Mathematical Reviews number (MathSciNet)
MR2408655

Citation

Cook, R. Dennis. Fisher Lecture: Dimension Reduction in Regression. Statist. Sci. 22 (2007), no. 1, 1--26. doi:10.1214/088342306000000682. http://projecteuclid.org/euclid.ss/1185975631.


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