Principal Fitted Components for Dimension Reduction in Regression

Details Principal Fitted Components for Dimension Reduction in Regression Principal Fitted Components for Dimension Reduction in Regression

2009-06-22

arxiv.org/abs/0906.3953v1

Statistical Science 2008, Vol. 23, No. 4, 485-501

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/08-STS275 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M

Scientific paper

10.1214/08-STS275

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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