Convergence of the empirical spectral distribution function of Beta matrices
Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral sta...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/80954 http://hdl.handle.net/10220/38995 |
| Summary: | Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral statistics of Bn. Especially, we do not require Sn or TN to be invertible. Namely, we can deal with the case where p>max{n,N} and p<n+N. Therefore, our results cover many important applications which cannot be simply deduced from the corresponding results for multivariate F matrices. |
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