Article ID Journal Published Year Pages File Type
1146109 Journal of Multivariate Analysis 2013 9 Pages PDF
Abstract

In this paper we demonstrate that a higher-ranking principal component of the predictor tends to have a stronger correlation with the response in single index models and sufficient dimension reduction. This tendency holds even though the orientation of the predictor is not designed in any way to be related to the response. This provides a probabilistic explanation of why it is often beneficial to perform regression on principal components—a practice commonly known as principal component regression but whose validity has long been debated. This result is a generalization of earlier results by Li (2007) [19], Artemiou and Li (2009) [2], and Ni (2011) [24], where the same phenomenon was conjectured and rigorously demonstrated for linear regression.

Related Topics
Physical Sciences and Engineering Mathematics Numerical Analysis
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