Self-consistency and principal component analysis

• 成果类型: Article
• 署名作者: Tarpey, T
• 署名单位: University System of Ohio; Wright State University Dayton
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2670166
• 发表日期: 1999
• 页码: 456-467
• 关键词: univariate distributions; points; asymptotics; quantizers; uniqueness; CURVES

摘要

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.