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.

DOI

10.2307/2670166

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