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 journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)760-768
Number of pages9
JournalAnnals of the Institute of Statistical Mathematics
Volume53
Issue number4
DOIs
Publication statusPublished - 2001
Externally publishedYes

Keywords

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

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