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Generalized Bayesian shrinkage and wavelet estimation of location parameter for spherical distribution under balance-type loss: Minimaxity and admissibility

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  • Karamikabir, Hamid
  • Afshari, Mahmoud

Abstract

One of the most important subject in multivariate analysis is parameters estimation. Among different methods, the shrinkage estimation is of interest. In this paper we consider the generalized Bayes shrinkage estimator of location parameter for spherical distribution under balance-type loss. We assume that the random vector having a spherical symmetric distribution with the known scalar variational component. Also, we find minimax and admissible estimator of location parameter based on generalized Bayes estimator. We investigate wavelet generalized Bayes estimator of location under balance-LINEX loss function. At the end, the performance evaluation of the proposed class of estimators is checked through a simulation study.

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  • 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).
    • Handle: RePEc:eee:jmvana:v:177:y:2020:i:c:s0047259x19303239
    DOI: 10.1016/j.jmva.2019.104583
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    References listed on IDEAS

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    1. Jafari Jozani, Mohammad & Marchand, Éric & Parsian, Ahmad, 2006. "On estimation with weighted balanced-type loss function," Statistics & Probability Letters, Elsevier, vol. 76(8), pages 773-780, April.
    2. Torehzadeh, S. & Arashi, M., 2014. "A note on shrinkage wavelet estimation in Bayesian analysis," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 231-234.
    3. Cao, Ming-Xiang & He, Dao-Jiang, 2017. "Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 246-254.
    4. Shokofeh Zinodiny & Sadegh Rezaei & Saralees Nadarajah, 2017. "Minimax Estimation of the Mean Matrix of the Matrix Variate Normal Distribution under the Divergence Loss Function," Statistica, Department of Statistics, University of Bologna, vol. 77(4), pages 369-384.
    5. Srivastava, M.S. & Ehsanes Saleh, A.K.Md., 2005. "Estimation of the mean vector of a multivariate normal distribution: subspace hypothesis," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 55-72, September.
    6. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    7. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2015. "Estimation of the mean vector in a singular multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 245-258.
    8. 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.
    9. M. Afshari & F. Lak & B. Gholizadeh, 2017. "A new Bayesian wavelet thresholding estimator of nonparametric regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 649-666, March.
    10. Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2012. "Bayesian and Robust Bayesian analysis under a general class of balanced loss functions," Statistical Papers, Springer, vol. 53(1), pages 51-60, February.
    11. Zinodiny, S. & Rezaei, S. & Nadarajah, S., 2017. "Bayes minimax estimation of the mean matrix of matrix-variate normal distribution under balanced loss function," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 110-120.
    12. Huang, Su-Yun, 2002. "On a Bayesian aspect for soft wavelet shrinkage estimation under an asymmetric Linex loss," Statistics & Probability Letters, Elsevier, vol. 56(2), pages 171-175, January.
    13. 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. 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.

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