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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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    Cited by:

    1. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Taras Bodnar & Nestor Parolya & Erik Thorsen, 2021. "Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio," Papers 2106.02131, arXiv.org, revised Nov 2021.
    3. 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 Apr 2023.
    4. Qiang, Beidi & Peña, Edsel A., 2023. "Robust simultaneous estimation of location parameters," Statistics & Probability Letters, Elsevier, vol. 193(C).
    5. 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.
    6. Yuasa, Ryota & Kubokawa, Tatsuya, 2020. "Ridge-type linear shrinkage estimation of the mean matrix of a high-dimensional normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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