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Gamma-minimax estimators for the mean of a multivariate normal distribution with partially unknown covariance matrix

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Abstract

In this paper Γ-minimax estimation of a multivariate normal mean under arbitrary squared error loss is considered where the covariance matrix of the normal distribution is a known symmetric and positive definite matrix with unknown multiple. The set Γ is fixed by imposing restrictions on the vector of first moments and on the matrix of second moments as well as on the first moment of the unknown factor determining of the covariance matrix. Necessary and sufficient conditions are derived which ensure that an estimator is Γ-minimax and that a prior is least favorable in Γ.

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, 200092, Shanghai, China

    Chen Lanxing

  2. Fachbereich Mathematik Technische Hochschule, Darmstadt, Germany

    Jürgen Lehn

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  1. Chen Lanxing
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  2. Jürgen Lehn
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Chen, L., Lehn, J. Gamma-minimax estimators for the mean of a multivariate normal distribution with partially unknown covariance matrix. Acta Mathematicae Applicatae Sinica 11, 11–16 (1995). https://doi.org/10.1007/BF02012618

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  • DOI: https://doi.org/10.1007/BF02012618

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