#### Title

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