Ignorance prior distribution of a hyperparameter and Stein's estimator

  • Hirotugu Akaike


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.


Posterior Distribution Prior Distribution Multivariate Normal Distribution Prior Density Admissible Estimator 


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© The Institute of Statistical Mathematics, Tokyo 1980

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  • Hirotugu Akaike

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