On combining correlated estimators of the common mean of a multivariate normal distribution

Abstract

The inferential procedures based on an optimal combination of correlated estimators of the common mean of a multivariate normal distribution are considered. Exact properties of the conditional and unconditional confidence intervals due to Halperin [Halperin, 1961, Almost linearly-optimum combination of unbiased estimates. Journal of the American Statistical Association, 56, 36–43] are numerically evaluated. Our numerical studies show that the conditional confidence interval is slightly shorter than the unconditional confidence interval. A condition under which the conditional approach is advantageous over the best of the t procedures based on individual components is discussed. The methods are illustrated using an example.

Keywords:

• Concomitant variable
• Expected length
• Maximum likelihood estimator
• Noncentral t distribution
• Multiple correlation coefficient
• Power

Acknowledgements

The authors are thankful to a referee for reviewing this article.