Abstract
Let X 1, θ, X n (n > p) be a random sample from multivariate normal distribution N p (μ, Σ), where μ ε R p and Σ is a positive definite matrix, both μ and Σ being unknown. We consider the problem of estimating the precision matrix Σ−1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of Σ−1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.
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Zhou, X., Sun, X. & Wang, J. Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss. Annals of the Institute of Statistical Mathematics 53, 760–768 (2001). https://doi.org/10.1023/A:1014657020370
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DOI: https://doi.org/10.1023/A:1014657020370