RDS free CLT for spiked eigenvalues of high-dimensional covariance matrices

Yan Liu, Zhidong Bai, Hua Li, Jiang Hu, Zhihui Lv and Shurong Zheng

Statistics & Probability Letters, 2022, vol. 187, issue C

Abstract: In this paper, we extend the CLT for sample spiked eigenvalues in the generalized spiked covariance model proposed in Jiang and Bai (2021a) to the case where RDS is considered free, i.e., except for an upper limit of the RDS to guarantee that the spiked eigenvalue is distant, there is no limit for p/n, which is the Ratio of Dimension to sample Size (RDS). Therefore, the choice of dimensionality and sample size is more flexible in our regime.

Keywords: High-dimensional covariance matrix; Random matrix theory; Spiked model; Central limit theorem; Ratio of Dimension to sample Size; Ultra-high dimension (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2022.109501

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