This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 35
Type: Contributed
Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract - #306779
Title: On the Predictive Potential of Kernel Principal Components
Author(s): Andreas Artemiou*+ and Bing Li
Companies: Penn State and Penn State
Address: 325 Thomas Building, University Park , PA, 16802,
Keywords: kernel principal components ; random covariance operator ; Cauchy distribution ; unitary invariance
Abstract:

In this paper we give a systematic probabilistic analysis of a phenomenon that is well known in statistics but until recently has no convincing explanation; that is, the first few principal components tend to possess predictive power for a response variable not designed in any way to be related to these principal components. We show that the phenomenon goes far beyond linear regression and principal components: if nature picks an arbitrary distribution for the predictor $X$ and an arbitrary conditional distribution of the response $Y$ given $X$, then $Y$ is more likely to have stronger correlation with higher-ranking kernel principal components than with lower-ranking kernel principal components. We formulate the ``arbitrariness'' by unitary invariance, and explicitly quantify the frequency of this tendency by exploring the relation between unitary invariance and the Cauchy distri


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