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On the best equivariant estimator of mean of a multivariate normal population

Author

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  • Perron, F.
  • Giri, N.

Abstract

Let X1,...,Xn (n>1, p>1) be independently and identically distributed normal p-vectors with mean [mu] and covariance matrix ([mu]'[mu]/C2)I, where the coefficient of variation C is known. The authors have obtained the best equivariant estimator of [mu] under the loss function L([mu]d)=([mu]-d)'([mu]-d/[mu]'[mu]) They have compared the best equivariant estimator with 3 other wellknown equivariant estimators of [mu] and have shown that the best equivariant estimator is markedly superior to others when C-->0.

Suggested Citation

  • Perron, F. & Giri, N., 1990. "On the best equivariant estimator of mean of a multivariate normal population," Journal of Multivariate Analysis, Elsevier, vol. 32(1), pages 1-16, January.
    • Handle: RePEc:eee:jmvana:v:32:y:1990:i:1:p:1-16
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    Cited by:

    1. Kanika, & Kumar, Somesh & SenGupta, Ashis, 2015. "A unified approach to decision-theoretic properties of the MLEs for the mean directions of several Langevin distributions," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 160-172.
    2. T. Leo Alexander & B. Chandrasekar, 2005. "Simultaneous equivariant estimation of the parameters of matrix scale and matrix location-scale models," Statistical Papers, Springer, vol. 46(4), pages 483-507, October.

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