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Estimation of the multivariate normal covariance matrix under some restrictions

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  • Sheena Yo
  • Gupta Arjun K.

Abstract

We consider the estimation of Σ of the p-dimensional normal distribution Np(0,Σ) under the restriction where the eigenvalues of Σ have an upper or lower bound. From a decision-theoretic point of view, we evaluate the performance of the REML (restricted maximum likelihood estimator) with Stein′s loss function and propose another estimator that dominates the REML.

Suggested Citation

  • Sheena Yo & Gupta Arjun K., 2003. "Estimation of the multivariate normal covariance matrix under some restrictions," Statistics & Risk Modeling, De Gruyter, vol. 21(4/2003), pages 327-342, April.
    • Handle: RePEc:bpj:strimo:v:21:y:2003:i:4/2003:p:327-342:n:3
    DOI: 10.1524/stnd.21.4.327.25349
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    References listed on IDEAS

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    1. Haff, L. R., 1979. "An identity for the Wishart distribution with applications," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 531-544, December.
    2. Haff, L. R., 1977. "Minimax estimators for a multinormal precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 374-385, September.
    3. Sheena, Yo & Takemura, Akimichi, 1992. "Inadmissibility of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss," Journal of Multivariate Analysis, Elsevier, vol. 41(1), pages 117-131, April.
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    Cited by:

    1. Maurya, Ashwini, 2014. "A joint convex penalty for inverse covariance matrix estimation," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 15-27.

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