Self-Consistency and Principal Component Analysis
Document Type
Article
Publication Date
1999
Abstract
I examine the self-consistency of a principal component axis; that is, when a distribution is centered about a principal component axis. A principal component axis of a random vector X is self-consistent if each point on the axis corresponds to the mean of X given that X projects orthogonally onto that point. A large class of symmetric multivariate distributions are examined in terms of self-consistency of principal component subspaces. Elliptical distributions are characterized by the preservation of self-consistency of principal component axes after arbitrary linear transformations. A "lack-of-fit" test is proposed that tests for self-consistency of a principal axis. The test is applied to two real datasets.
Repository Citation
Tarpey, T.
(1999). Self-Consistency and Principal Component Analysis. Journal of the American Statistical Association, 94 (446), 456-467.
https://corescholar.libraries.wright.edu/math/192
DOI
10.2307/2670166
