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The asymptotic expansion fo the Stein estimators for the vector case

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Summary

Charles Stein established the existence of estimators which dominate the maximum likelihood estimators for the problem of simultanously estimating the means of three or more random variables.

Since the exact distributions of the Stein estimators are not known and because the distributions are of great importance for people studying confidence sets, it was the purpose of this note to derive the asymptotic distributions, means and variances of the Stein estimators, as well as that of the quadratic loss functions for the vector case.

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References

  1. de Bruijn, N. G. (1958).Asymptotic Methods in Analysis, North-Holland Publishing Company.

  2. James, W. and Stein, C. (1961). Estimation with quadratic loss,Proc. Fourth Berkeley Symp. Math. Statist., Prob., Vol. I, University of California Press, 361–379.

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Authors and Affiliations

  1. University of the Orange Free State, Bloemfontein, South Africa

    A. J. van der Merwe & D. J. de Waal

Authors
  1. A. J. van der Merwe
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  2. D. J. de Waal
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Financially supported by the CSIR and the University of the OFS Research Fund.

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van der Merwe, A.J., de Waal, D.J. The asymptotic expansion fo the Stein estimators for the vector case. Ann Inst Stat Math 30, 385–395 (1978). https://doi.org/10.1007/BF02480228

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  • DOI: https://doi.org/10.1007/BF02480228

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