Estimation of the multivariate normal precision matrix under the entropy loss

Xian Zhou; Xiaoqian Sun; Jinglong Wang

doi:10.1023/A:1014657020370

Estimation of the multivariate normal precision matrix under the entropy loss

Xian Zhou^*, Xiaoqian Sun, Jinglong Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

Let X₁,...,X_n(n > p) be a random sample from multivariate normal distribution N_p(μ, Σ), where μ ∈ 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.

Original language	English
Pages (from-to)	760-768
Number of pages	9
Journal	Annals of the Institute of Statistical Mathematics
Volume	53
Issue number	4
DOIs	https://doi.org/10.1023/A:1014657020370
Publication status	Published - 2001
Externally published	Yes

Keywords

Best lower-triangular equivariant minimax estimator
Inadmissibility
Multivariate normal distribution
Precision matrix
Risk function
The entropy loss

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author = "Xian Zhou and Xiaoqian Sun and Jinglong Wang",

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AU - Zhou, Xian

AU - Sun, Xiaoqian

AU - Wang, Jinglong

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AB - Let X1,...,Xn(n > p) be a random sample from multivariate normal distribution Np(μ, Σ), where μ ∈ Rp 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.

KW - Best lower-triangular equivariant minimax estimator

KW - Inadmissibility

KW - Multivariate normal distribution

KW - Precision matrix

KW - Risk function

KW - The entropy loss

UR - https://www.scopus.com/pages/publications/6644219760

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DO - 10.1023/A:1014657020370

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EP - 768

JO - Annals of the Institute of Statistical Mathematics

JF - Annals of the Institute of Statistical Mathematics

IS - 4

ER -

Estimation of the multivariate normal precision matrix under the entropy loss

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Keywords

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