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Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices

Author

Listed:
  • Wang, Cheng
  • Tong, Tiejun
  • Cao, Longbing
  • Miao, Baiqi

Abstract

In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric distribution for the data and it does not require the prior information on the population covariance matrix. Analytical results on the improvement of the proposed shrinkage estimator are provided and some corresponding asymptotic properties are also derived. Finally, we demonstrate the practical improvement of the proposed method over existing methods through extensive simulation studies and real data analysis.

Suggested Citation

  • Wang, Cheng & Tong, Tiejun & Cao, Longbing & Miao, Baiqi, 2014. "Non-parametric shrinkage mean estimation for quadratic loss functions with unknown covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 222-232.
  • Handle: RePEc:eee:jmvana:v:125:y:2014:i:c:p:222-232
    DOI: 10.1016/j.jmva.2013.12.012
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    4. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    5. Hwang J.T. Gene & Liu Peng, 2010. "Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-35, October.
    6. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    7. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, December.
    8. Fourdrinier, Dominique & Strawderman, William E. & Wells, Martin T., 2003. "Robust shrinkage estimation for elliptically symmetric distributions with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 24-39, April.
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    Cited by:

    1. Taras Bodnar & Holger Dette & Nestor Parolya & Erik Thors'en, 2019. "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions," Papers 1908.04243, arXiv.org, revised Aug 2019.
    2. 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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