Fisher Lecture: Dimension Reduction in Regression
Top Cited Papers
Open Access
- 1 February 2007
- journal article
- Published by Institute of Mathematical Statistics in Statistical Science
- Vol. 22 (1) , 1-26
- https://doi.org/10.1214/088342306000000682
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.Keywords
All Related Versions
This publication has 55 references indexed in Scilit:
- Sufficient Dimension Reduction via Inverse RegressionJournal of the American Statistical Association, 2005
- Principal Components Regression With Data Chosen Components and Related MethodsTechnometrics, 2003
- Some Cautionary Notes on the Use of Principal Components RegressionThe American Statistician, 1998
- Sliced Inverse Regression for Dimension ReductionJournal of the American Statistical Association, 1991
- Random Calibration With Many Measurements: An Application of Stein EstimationTechnometrics, 1991
- Role of Models in Statistical AnalysisStatistical Science, 1990
- Principal component estimation for generalized linear regressionBiometrika, 1990
- On Rereading R. A. FisherThe Annals of Statistics, 1976
- Analysis of a complex of statistical variables into principal components.Journal of Educational Psychology, 1933
- III. The influence of rainfall on the yield of wheat at RothamstedPhilosophical Transactions of the Royal Society of London. Series B, Containing Papers of a Biological Character, 1925