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Improved minimax estimation of a normal precision matrix
Author(s) -
Krishnamoorthy K.,
Gupta A. K.
Publication year - 1989
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314766
Subject(s) - wishart distribution , estimator , mathematics , minimax , invariant (physics) , combinatorics , multivariate normal distribution , monte carlo method , statistics , multivariate statistics , mathematical optimization , mathematical physics
Let S p × p have a Wishart distribution with parameter matrix Σ and n degrees of freedom. We consider here the problem of estimating the precision matrix Σ −1 under the loss functions L 1 (σ) tr (σ) ‐ log |σ| and L 2 (σ) = tr (σ). James‐Stein‐type estimators have been derived for an arbitrary p . We also obtain an orthogonal invariant and a diagonal invariant minimax estimator under both loss functions. A Monte‐Carlo simulation study indicates that the risk improvement of the orthogonal invariant estimators over the James‐Stein type estimators, the Haff (1979) estimator, and the “testimator” given by Sinha and Ghosh (1987) is substantial.