A geometric framework for asymptotic inference of principal subspaces in PCA
Résumé
Consider data assumed to be iid samples from a multivariate Gaussian distribution whose covariance matrix has repeated eigenvalues. In our model, these eigenvalues are unknown but their multiplicities are supposed to be known. In this paper, we develop an asymptotic method to infer the collection of all principal subspaces together, i.e. the eigenspaces of this covariance matrix. Our approach is based on the geometry of the flag manifold to which the collection of all principal subspaces and our estimators of it belong.
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