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

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.From our work, the limitation of RDS for the CLT for spiked eigenvalues of the sample covariance matrix under usual high-dimensional settings is removed, and the ultra-high dimensional regime is also covered as a special case.