Showing papers by "William E. Strawderman published in 1973"

Proper Bayes Minimax Estimators of the Multivariate Normal Mean Vector for the Case of Common Unknown Variances

Abstract: We investigate the problem of estimating the mean vector $\mathbf{\theta}$ of a multivariate normal distribution with covariance matrix equal to $\sigma^2\mathbf{I}_p, \sigma^2$ unknown, and loss $\|\delta - \mathbf{\theta}\|^2/\sigma^2$. We first find a class of minimax estimators for this problem which enlarges a class given by Baranchik. This result is then used to show that for sufficiently large sample sizes (which never need exceed 4) proper Bayes minimax estimators exist for $\mathbf{\theta}$ if $p \geqq 5$.

Admissibility Implications for Different Criteria in Confidence Estimation

Abstract: It will be shown that if a confidence procedure is admissible when the criterion is probability of not covering the true value and expected length (or something more general than length), then the same confidence procedure is at least almost admissible when the criterion is probability of not covering the true value and probability of covering false values. The result is true (under mild conditions) for virtually all confidence region estimation problems.