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Bayesian Statistical Inference on Elliptical Matrix Distributions

Author

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  • Fang, Kai-Tai
  • Li, Runze

Abstract

In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters[mu]and[Sigma]. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators of[mu]and[Sigma]. Under the entropy loss and quadratic loss, the best Bayesian estimators of[Sigma]are derived as well. Some applications are given.

Suggested Citation

  • Fang, Kai-Tai & Li, Runze, 1999. "Bayesian Statistical Inference on Elliptical Matrix Distributions," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 66-85, July.
    • Handle: RePEc:eee:jmvana:v:70:y:1999:i:1:p:66-85
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    Cited by:

    1. Chung, Hee Cheol & Ahn, Jeongyoun, 2021. "Subspace rotations for high-dimensional outlier detection," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Fernández, Carmen & Osiewalski, Jacek & Steel, Mark F. J., 2001. "Robust Bayesian Inference on Scale Parameters," Journal of Multivariate Analysis, Elsevier, vol. 77(1), pages 54-72, April.
    3. Kibria, B.M. Golam, 2006. "The matrix-t distribution and its applications in predictive inference," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 785-795, March.
    4. Díaz-García, José A. & Gutiérrez-Jáimez, Ramón, 2011. "Distributions of the compound and scale mixture of vector and spherical matrix variate elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 143-152, January.
    5. M. Arashi & B. Kibria & A. Tajadod, 2015. "On shrinkage estimators in matrix variate elliptical models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 29-44, January.
    6. Mário Castro & Ignacio Vidal, 2019. "Bayesian inference in measurement error models from objective priors for the bivariate normal distribution," Statistical Papers, Springer, vol. 60(4), pages 1059-1078, August.
    7. Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.
    8. Jiang, Jie & Wang, Lichun, 2024. "Bayes minimax estimator of the mean vector in an elliptically contoured distribution," Statistics & Probability Letters, Elsevier, vol. 213(C).

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