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Ignorance prior distribution of a hyperparameter and Stein's estimator

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Summary

The concept of ignorance prior distribution is extended to the case of a hyperparameter. This leads to a procedure of formulating the partial ignorance of the original parameter. Its application to the estimation of the mean of a multivariate normal distribution with a particular hyperparameterized prior distribution of the mean leads to an improper prior distribution with the corresponding posterior mean very close to the James-Stein estimate.

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References

  1. Akaike, H. (1978). A new look at the Bayes procedure,Biometrika,65, 53–59.

    Article  MathSciNet  Google Scholar 

  2. Brown, L. D. (1971). Admissible estimators, recurrent diffusions, and insoluble boundary value problem.Ann. Math. Statist.,42, 855–903.

    Article  MathSciNet  Google Scholar 

  3. Efron, B. (1978). Controversies in the foundation of statistics,Amer. Math. Monthly,85, 231–246.

    Article  MathSciNet  Google Scholar 

  4. Jeffreys, H. (1961).Theory of Probability, 3rd ed., Oxford University Press, London.

    MATH  Google Scholar 

  5. Stein, C. (1962). Confidence sets for the mean of a multivariate normal distribution,J. R. Statist, Soc., B,24, 265–296.

    MathSciNet  MATH  Google Scholar 

  6. Stein, C. (1973). Estimation of the mean of a multivariate normal distribution,Proceeding of the Prague Symposium on Asymptotic Statistics, 345–381.

  7. Strawderman, W. E. (1971). Proper Bayes minimax estimators of the multivariate normal mean.Ann. Math. Statist.,42, 385–388.

    Article  MathSciNet  Google Scholar 

  8. Takada, Y. (1979). Stein's positive part estimator and Bayes estimator,Ann. Inst. Statist. Math.,31, A, 177–183.

    Article  MathSciNet  Google Scholar 

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Authors
  1. Hirotugu Akaike
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The Institute of Statistical Mathematics

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Akaike, H. Ignorance prior distribution of a hyperparameter and Stein's estimator. Ann Inst Stat Math 32, 171–178 (1980). https://doi.org/10.1007/BF02480322

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  • DOI: https://doi.org/10.1007/BF02480322

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