Ignorance prior distribution of a hyperparameter and Stein's estimator
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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.
KeywordsPosterior Distribution Prior Distribution Multivariate Normal Distribution Prior Density Admissible Estimator
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- Stein, C. (1973). Estimation of the mean of a multivariate normal distribution,Proceeding of the Prague Symposium on Asymptotic Statistics, 345–381.Google Scholar