Self-Consistency and Principal Component Analysis
研究了主成分轴的自洽性，即分布关于主成分轴中心对称的性质，提出了检验主成分轴自洽性的缺乏拟合检验，并应用于两个真实数据集。
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.