Preliminary test estimation for multi-sample principal components

Point estimation is considered in a multi-sample principal components setup, in a situation where it is suspected that the hypothesis of common principal components (CPC) holds. Preliminary test estimators of the various principal eigenvectors are proposed. Their asymptotic distributions are derived (i) under the CPC hypothesis, (ii) under sequences of hypotheses that are contiguous to the CPC hypothesis, and (iii) away from the CPC hypothesis. A Monte-Carlo study shows that the proposed estimators perform well, particularly so in the Gaussian case.