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Institute for Research in Computer Science and Random Systems |  |
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Institute for Research in Computer Science and Random Systems | |
| HAL: hal-00565149, version 1 |
| DOI: 10.1111/j.1467-842X.2010.00590.x |
| Detailed view |  Export this paper |
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| Australian & New Zealand Journal of Statistics 52, 4 (2010) 423-437 |
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| On estimation of the population spectral distribution from a high-dimensional sample covariance matrix |
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| Zhidong Bai 1, 2Jiaqi Chen |
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| (2010) |
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| Sample covariance matrices play a central role in numerous popular statistical methodologies, for example principal components analysis, Kalman filtering and independent component analysis. However, modern random matrix theory indicates that, when the dimension of a random vector is not negligible with respect to the sample size, the sample covariance matrix demonstrates significant deviations from the underlying population covariance matrix. There is an urgent need to develop new estimation tools in such cases with high-dimensional data to recover the characteristics of the population covariance matrix from the observed sample covariance matrix. We propose a novel solution to this problem based on the method of moments. When the parametric dimension of the population spectrum is finite and known, we prove that the proposed estimator is strongly consistent and asymptotically Gaussian. Otherwise, we combine the first estimation method with a cross-validation procedure to select the unknown model dimension. Simulation experiments demonstrate the consistency of the proposed procedure. We also indicate possible extensions of the proposed estimator to the case where the population spectrum has a density. |
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| 1: | Key Laboratory of Applied Statistics under Ministry of Education (KLASMOE) |
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Northeast Normal University |
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| 2: | Department of Statistics and Applied Probability (DSAP) |
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National University of Singapore |
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| 3: | VISTAS (INRIA - IRISA) |
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INRIA – Institut National des Sciences Appliquées (INSA) - Rennes – CNRS : UMR6074 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan |
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| 4: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Subject | : | Mathematics/Statistics Statistics/Statistics Theory |
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| eigenvalues of covariance matrices – high-dimensional statistics – Marčenko–Pastur distribution – sample covariance matrices |
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| hal-00565149, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00565149 | |
| oai:hal.archives-ouvertes.fr:hal-00565149 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Friday, 11 February 2011 10:25:35 | |
| Updated on: Friday, 11 February 2011 10:25:35 | |
