PCA Consistency for Non-Gaussian Data in High Dimension Low Sample Size Context

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In this article, we investigate both sample eigenvalues and Principal Component (PC) directions along with PC scores when the dimension d and the sample size n both grow to infinity in such a way that n is much lower than d. We consider general settings that include the case when the eigenvalues are all in the range of sphericity. We do not assume either the normality or a ρ-mixing condition. We attempt finding a difference among the eigenvalues by choosing n with a suitable order of d. We give the consistency properties for both the sample eigenvalues and the PC directions along with the PC scores. We also show that the sample eigenvalue has a Gaussian limiting distribution when the population counterpart is of multiplicity one.

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