Continuity and Analysis of Sequences of Principal Components
Double arrays of n rows and p columns can be regarded as n drawings from some p-dimensional population. A sequence of such arrays is considered. Principal component analysis for each array forms sequences of sample principal components and eigenvalues. The continuity of these sequences, in the sense of convergence with probability one and convergence in probability, is investigated, that appears to be informative for pattern study and prediction of principal components. Various features of paths of sequences of population principal components are highlighted through an example.