Repeatability of Principal Components in Samples: Normal and Non-Normal Data Sets Compared

Abstract

The asymptotic theory of the distribution of the latent roots and vector of principal components analysis (PCA) of samples has hitherto been tied t multivariate normal (MVN) distributions. However, much real behavior dat are not normal. The results of the present study show, using arguments base on Monte Carlo methods, that if there is enough meaningful structure in th population, then PCA of samples of data with multivariate non-normal (NN distribution may provide answers relative to the "true" population principal components (PC) of comparable reliability to PCA of samples of MVAT data.