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November 2008 Principal Fitted Components for Dimension Reduction in Regression
R. Dennis Cook, Liliana Forzani
Statist. Sci. 23(4): 485-501 (November 2008). DOI: 10.1214/08-STS275

Abstract

We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components [Cook, R. D. (2007). Fisher lecture: Dimension reduction in regression (with discussion). Statist. Sci. 22 1–26] and uses normal models for the inverse regression of the predictors on the response to gain reductive information for the forward regression of interest. This approach includes methodology for testing hypotheses about the number of components and about conditional independencies among the predictors.

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R. Dennis Cook. Liliana Forzani. "Principal Fitted Components for Dimension Reduction in Regression." Statist. Sci. 23 (4) 485 - 501, November 2008. https://doi.org/10.1214/08-STS275

Information

Published: November 2008
First available in Project Euclid: 11 May 2009

zbMATH: 1329.62274
MathSciNet: MR2530547
Digital Object Identifier: 10.1214/08-STS275

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.23 • No. 4 • November 2008
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