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Bayesian Wavelet Stein’s Unbiased Risk Estimation of Multivariate Normal Distribution Under Reflected Normal Loss

Author

Listed:
  • Hamid Karamikabir

    (Persian Gulf University)

  • Nasrin Karamikabir

    (Hamedan Branch, Islamic Azad University)

  • Mohammad Ali Khajeian

    (Persian Gulf University)

  • Mahmoud Afshari

    (Persian Gulf University)

Abstract

In this paper, we consider the generalized Bayes estimator of mean vector parameter for multivariate normal distribution with unknown mean vector and covariance matrix under reflected normal loss function. We also prove admissibility and minimaxity of the generalized Bayes estimator. We obtain Stein’s unbiased risk estimator (SURE) threshold based on generalized Bayes SURE estimator and we find the wavelet shrinkage generalized Bayes SURE estimator. At the end, we check the performance of this estimator and we provide two real examples.

Suggested Citation

  • Hamid Karamikabir & Nasrin Karamikabir & Mohammad Ali Khajeian & Mahmoud Afshari, 2023. "Bayesian Wavelet Stein’s Unbiased Risk Estimation of Multivariate Normal Distribution Under Reflected Normal Loss," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-20, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-09992-3
    DOI: 10.1007/s11009-023-09992-3
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    References listed on IDEAS

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    1. Dominique Fourdrinier & William Strawderman, 2015. "Robust minimax Stein estimation under invariant data-based loss for spherically and elliptically symmetric distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(4), pages 461-484, May.
    2. Karamikabir, Hamid & Afshari, Mahmoud, 2020. "Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility," Journal of Multivariate Analysis, Elsevier, vol. 177(C).
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