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Bayesian estimation of a bounded precision matrix

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  • Tsukuma, Hisayuki

Abstract

The inverse of normal covariance matrix is called precision matrix and often plays an important role in statistical estimation problem. This paper deals with the problem of estimating the precision matrix under a quadratic loss, where the precision matrix is restricted to a bounded parameter space. Gauss’ divergence theorem with matrix argument shows that the unbiased and unrestricted estimator is dominated by a posterior mean associated with a flat prior on the bounded parameter space. Also, an improving method is given by considering an expansion estimator. A hierarchical prior is shown to improve on the posterior mean. An application is given for a Bayesian prediction in a random-effects model.

Suggested Citation

  • Tsukuma, Hisayuki, 2014. "Bayesian estimation of a bounded precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 160-172.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:160-172
    DOI: 10.1016/j.jmva.2014.02.016
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    References listed on IDEAS

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    1. Kubokawa, Tatsuya & Srivastava, Muni S., 2008. "Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1906-1928, October.
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    5. Xian Zhou & Xiaoqian Sun & Jinglong Wang, 2001. "Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 760-768, December.
    6. Haff, L. R., 1977. "Minimax estimators for a multinormal precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 374-385, September.
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