Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix

Wonjun Seo

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arXiv · 2604.26178

Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix

Wonjun Seo

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Abstract

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^{\alpha} $, $ \alpha > 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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Wonjun Seo. 2026-04-28. Asymptotics of ultra-high-dimensional generalized spiked sample covariance matrix. https://arxiv.org/abs/2604.26178

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