Preliminary Test Estimation for Multi-Sample Principal Components

In this paper, we consider point estimation in a multi-sample principal components setup, in a situation where it is suspected that the hypothesis of common principal components (CPC) holds. We propose preliminary test estimators of the various principal eigenvectors. We derive their asymptotic distributions (i) under the CPC hypothesis, (ii) under sequences of hypotheses that are contiguous to the CPC hypothesis, and (iii) away from the CPC hypothesis. We conduct a Monte-Carlo study that shows that the proposed estimators perform well, particularly so in the Gaussian case.