CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size
Let A = 1/√np(XT X−pIn) where X is a p×n matrix, consisting of independent and identically distributed (i.i.d.) real random variables Xij with mean zero and variance one. When p/n→∞, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2015
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| Online Access: | https://hdl.handle.net/10356/107446 http://hdl.handle.net/10220/25620 |
| _version_ | 1824453645220970496 |
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| author | Chen, Binbin Pan, Guangming |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Chen, Binbin Pan, Guangming |
| author_sort | Chen, Binbin |
| collection | NTU |
| description | Let A = 1/√np(XT X−pIn) where X is a p×n matrix, consisting of independent and identically distributed (i.i.d.) real random variables Xij with mean zero and variance one. When p/n→∞, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix. |
| first_indexed | 2025-02-19T03:09:42Z |
| format | Journal Article |
| id | ntu-10356/107446 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:09:42Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | ntu-10356/1074462023-02-28T19:47:37Z CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size Chen, Binbin Pan, Guangming School of Physical and Mathematical Sciences DRNTU::Science::Physics::Atomic physics Let A = 1/√np(XT X−pIn) where X is a p×n matrix, consisting of independent and identically distributed (i.i.d.) real random variables Xij with mean zero and variance one. When p/n→∞, under fourth moment conditions a central limit theorem (CLT) for linear spectral statistics (LSS) of A defined by the eigenvalues is established. We also explore its applications in testing whether a population covariance matrix is an identity matrix. Published version 2015-05-20T03:46:00Z 2019-12-06T22:31:18Z 2015-05-20T03:46:00Z 2019-12-06T22:31:18Z 2015 2015 Journal Article Chen, B., & Pan, G. (2015). CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size. Bernoulli, 21(2), 1089-1133. 1350-7265 https://hdl.handle.net/10356/107446 http://hdl.handle.net/10220/25620 10.3150/14-BEJ599 en Bernoulli © 2015 Bernoulli Society for Mathematical Statistics and Probability. This paper was published in Bernoulli and is made available as an electronic reprint (preprint) with permission of Bernoulli Society for Mathematical Statistics and Probability. The paper can be found at the following official DOI: [http://dx.doi.org/10.3150/14-BEJ599]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf |
| spellingShingle | DRNTU::Science::Physics::Atomic physics Chen, Binbin Pan, Guangming CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| title | CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| title_full | CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| title_fullStr | CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| title_full_unstemmed | CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| title_short | CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| title_sort | clt for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size |
| topic | DRNTU::Science::Physics::Atomic physics |
| url | https://hdl.handle.net/10356/107446 http://hdl.handle.net/10220/25620 |
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