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Estimation of the population spectral distribution from a large dimensional sample covariance matrix |
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| Authors: | Weiming Li Jiaqi Chen Yingli Qin Zhidong Bai Jianfeng Yao |
| Affiliation: | 1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;2. Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;3. Department of Statistics and Actuarial Science, University of Waterloo, Canada;4. KLAS MOE and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;5. Department of Statistics and Applied Probability, National University of Singapore, Singapore;6. Department of Statistics and Actuarial Science, The University of Hong Kong, Hongkong, China |
| Abstract: | This paper introduces a new method to estimate the spectral distribution of a population covariance matrix from high-dimensional data. The method is founded on a meaningful generalization of the seminal Mar?enko–Pastur equation, originally defined in the complex plane, to the real line. Beyond its easy implementation and the established asymptotic consistency, the new estimator outperforms two existing estimators from the literature in almost all the situations tested in a simulation experiment. An application to the analysis of the correlation matrix of S&P 500 daily stock returns is also given. |
| Keywords: | Empirical spectral distribution High-dimensional data analysis Mar?enko&ndash Pastur distribution Large sample covariance matrices Stieltjes transform |
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