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Shrinkage Efficiency Bounds

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  • Hansen, Bruce E.

Abstract

This paper is an extension of Magnus (2002, Econometrics Journal 5, 225–236) to multiple dimensions. We consider estimation of a multivariate normal mean under sum of squared error loss. We construct the efficiency bound (the lowest achievable risk) for minimax shrinkage estimation in the class of minimax orthogonally invariate estimators satisfying the sufficient conditions of Efron and Morris (1976, Annals of Statistics 4, 11–21). This allows us to compare the regret of existing orthogonally invariate shrinkage estimators. We also construct a new shrinkage estimator which achieves substantially lower maximum regret than existing estimators.

Suggested Citation

  • Hansen, Bruce E., 2015. "Shrinkage Efficiency Bounds," Econometric Theory, Cambridge University Press, vol. 31(4), pages 860-879, August.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:04:p:860-879_00
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    Cited by:

    1. Niels Wesselhöfft & Wolfgang K. Härdle, 2020. "Risk-Constrained Kelly Portfolios Under Alpha-Stable Laws," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 801-826, March.
    2. Giuseppe Luca & Jan R. Magnus, 2021. "Weak Versus Strong Dominance of Shrinkage Estimators," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 239-266, December.
    3. Wesselhöfft, Niels & Härdle, Wolfgang Karl, 2019. "Constrained Kelly portfolios under alpha-stable laws," IRTG 1792 Discussion Papers 2019-004, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Hansen, Bruce E., 2016. "Efficient shrinkage in parametric models," Journal of Econometrics, Elsevier, vol. 190(1), pages 115-132.
    5. Edvard Bakhitov, 2020. "Frequentist Shrinkage under Inequality Constraints," Papers 2001.10586, arXiv.org.

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