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Gaussian fluctuations for sample covariance matrices with dependent data

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  • Friesen, Olga
  • Löwe, Matthias
  • Stolz, Michael

Abstract

It is known (Hofmann-Credner and Stolz (2008) [4]) that the convergence of the mean empirical spectral distribution of a sample covariance matrix Wn=1/nYnYnt to the Marčenko–Pastur law remains unaffected if the rows and columns of Yn exhibit some dependence, where only the growth of the number of dependent entries, but not the joint distribution of dependent entries needs to be controlled. In this paper we show that the well-known CLT for traces of powers of Wn also extends to the dependent case.

Suggested Citation

  • Friesen, Olga & Löwe, Matthias & Stolz, Michael, 2013. "Gaussian fluctuations for sample covariance matrices with dependent data," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 270-287.
    • Handle: RePEc:eee:jmvana:v:114:y:2013:i:c:p:270-287
    DOI: 10.1016/j.jmva.2012.08.004
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    References listed on IDEAS

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    1. Jonsson, Dag, 1982. "Some limit theorems for the eigenvalues of a sample covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 1-38, March.
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    1. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2018. "Estimation of the global minimum variance portfolio in high dimensions," European Journal of Operational Research, Elsevier, vol. 266(1), pages 371-390.
    2. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2016. "Direct shrinkage estimation of large dimensional precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 223-236.
    3. Taras Bodnar & Yarema Okhrin & Nestor Parolya, 2022. "Optimal Shrinkage-Based Portfolio Selection in High Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 140-156, December.
    4. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.

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