RANDOM ERROR BIAS IN PRINCIPAL COMPONENT ANALYSIS .2. APPLICATION OF THEORETICAL PREDICTIONS TO MULTIVARIATE PROBLEMS

In the first part of this paper expressions were derived for the predi ction of random error bias in the eigenvalues of principal component a nalysis (PCA) and the singular values of singular value decomposition (SVD). The main issues of Part I were to investigate the question whet her adequate prediction of this bias is possible and to discuss how th e validation and evaluation of these predictions could proceed for a s pecific application in practice. The main issue of this second part is to investigate how random error bias should be taken into account. Th is question will be treated for a number of seemingly disparate multiv ariate problems. For example, the construction of confidence intervals for the bias-corrected quantities will be discussed with respect to t he estimation of the number of significant principal components. The c onsequences of random error bias for calibration and prediction with o rdinary least squares (OLS), principal component regression (PCR), par tial least squares (PLS) and the generalized rank annihilation method (GRAM) will also be outlined. Finally, the derived bias expressions wi ll be compared in detail with the corresponding results for OLS and GR AM.