Year: 2009
Type: article
Abstract: In this note we give a probabilistic explanation of a phenomenon that is \nfrequently observed but whose reason is not well understood. That is, in a regression \nsetting, the response (Y ) is often highly correlated with the leading principal \ncomponents of the predictor (X) even though there seems no logical reason for this \nconnection. This phenomenon has long been noticed and discussed in the literature, \nand has received renewed interest recently because of the need for regressing Y on \nX of very high dimension, often with comparatively few sampling units, in which \ncase it seems natural to regress on the first few principal components of X. This \nwork stems from a discussion of a recent paper by Cook (2007) which, along with \nother developments, described a historical debate surrounding, and current interest \nin, this phenomenon.
Authors: Andreas Artemiou, Bing Li
Institution: Pennsylvania State University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2289946858