Fisher Lecture: Dimension Reduction in Regression

Details Fisher Lecture: Dimension Reduction in Regression Fisher Lecture: Dimension Reduction in Regression

2007-08-28

arxiv.org/abs/0708.3774v1

Statistical Science 2007, Vol. 22, No. 1, 1-26

Statistics

Methodology

This paper commented in: [arXiv:0708.3776], [arXiv:0708.3777], [arXiv:0708.3779]. Rejoinder in [arXiv:0708.3781]. Published at

Scientific paper

10.1214/088342306000000682

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.

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