We study the problem of estimating the leading eigenvectors of a highdimensional population covariance matrix based on independent Gaussian observations. We establish a lower bound on the minimax risk of estimators under the l2 loss, in the joint limit as dimension and sample size increase to infinity, under various models of sparsity for the population eigenvectors. The lower bound on the risk...

Principal components analysis (PCA) of waveforms and functional PCA (fPCA) are statistical approaches used to explore patterns variability in biomechanical curve data, with fPCA being an accepted method grounded within the data (FDA) framework. This technical note demonstrates that is most rudimentary form FDA, consequently can be rationalised FDA framework processes. Mathematical proofing appl...

Phylogenetic PCA (p-PCA) is a version of for observations that are leaf nodes phylogenetic tree. P-PCA accounts the fact such not independent, due to shared evolutionary history. The method works on Euclidean data, but in biology there need applying it data manifolds, particularly shapes. We provide generalization p-PCA lying Riemannian called Tangent p-PCA. thus makes possible perform dimensio...