A note on sensitivity of principal component subspaces and the efficient detection of influential observations in high dimensions

In this paper we introduce an influence measure based on second order expansion of the RV and GCD measures for the comparison between unperturbed and perturbed eigenvectors of a symmetric matrix estimator. Example estimators are considered to highlight how this measure compliments recent influence analysis. Importantly, we also show how a sample based version of this measure can be used to accurately and efficiently detect influential observations in practice. AMS 2000 subject classifications: Primary 62F35; secondary 62H12.