Comparison of Experiments via Dependence of Normal Variables with a Common Marginal Distribution

Abstract

In this note we study comparison of experiments via the positive dependence of normal variables with a common univariate marginal distribution. We show that positive dependence has an adverse effect on the information concerning the common mean $\theta$, and give a partial ordering of the information via a majorization ordering of the correlation matrices. In the special case when the random variables are equally correlated, the main theorem yields a result for the comparison of experiments for permutation symmetric normal variables.