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Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix
Wonjun Seo · 2026-04-29 · via math.ST updates on arXiv.org

This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow much faster than the sample size with $ p \asymp n^α $, $ α> 1 $. We establish the first-order convergence limits of eigenvalue locations and eigenvector projections of properly scaled sample covariance matrix. Our results are extensions of \cite{bloemendal16,ding21}.

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