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Minimax covariance estimation using commutator subgroup of lower triangular matrices

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  • Tsukuma, Hisayuki

Abstract

This paper deals with the problem of estimating the normal covariance matrix relative to the Stein loss. The main interest concerns a new class of estimators which are invariant under a commutator subgroup of lower triangular matrices. The minimaxity of a James–Stein type invariant estimator under the subgroup is shown by means of a least favorable sequence of prior distributions. The class yields improved estimators on the James–Stein type invariant and minimax estimator.

Suggested Citation

  • Tsukuma, Hisayuki, 2014. "Minimax covariance estimation using commutator subgroup of lower triangular matrices," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 333-344.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:333-344
    DOI: 10.1016/j.jmva.2013.11.007
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    References listed on IDEAS

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    1. Ghosh M. & Sinha B. K., 1987. "Inadmissibility Of The Best Equivariant Estimators Of The Variance-Covariance Matrix, The Precision Matrix, And The Generalized Variance Under Entropy Loss," Statistics & Risk Modeling, De Gruyter, vol. 5(3-4), pages 201-228, April.
    2. Toma, Aida & Leoni-Aubin, Samuela, 2013. "Optimal robust M-estimators using Rényi pseudodistances," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 359-373.
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    Cited by:

    1. Tsukuma, Hisayuki, 2016. "Minimax estimation of a normal covariance matrix with the partial Iwasawa decomposition," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 190-207.

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