# A CLT for the LSS of large dimensional sample covariance matrices with unbounded dispersions

@inproceedings{Liu2022ACF, title={A CLT for the LSS of large dimensional sample covariance matrices with unbounded dispersions}, author={Zhijun Liu and Jiang Hu and Zhidong Bai and Haiyan Song}, year={2022} }

In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a non-trivial extension of the Bai-Silverstein theorem (BST) (2004). The latter has strongly stimulated the development of high-dimensional statistics, especially the application of random matrix theory to statistics. However, the assumption of uniform boundedness of the…

## 2 Citations

### Central limit theorem for eigenvalue statistics of sample covariance matrix with random population

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The case that Σ is random is considered and it is shown that theuctuation of converges in distribution to a Gaussian distribution, which implies that the randomness of Σ decreases the correlation among { λ i } .

### Quantitative limit theorems and bootstrap approximations for empirical spectral projectors

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Given finite i.i.d. samples in a Hilbert space with zero mean and trace-class covariance operator Σ, the problem of recovering the spectral projectors of Σ naturally arises in many applications. In…

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