Dimension estimation in PCA model using high-dimensional data augmentation

We propose a modified, high-dimensional version of a recent dimension estimation procedure that determines the dimension via the introduction of augmented noise variables into the data. Our asymptotic results show that the proposal is consistent in wide high-dimensional scenarios, and further shed light on why the original method breaks down when the dimension of either the data or the augmentation becomes too large. Simulations are used to demonstrate the superiority of the proposal to competitors both under and outside of the theoretical model.