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Comparison of experiments via dependence of normal variables with a common marginal distribution. (English) Zbl 0745.62006

Summary: 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.

MSC:

62B15 Theory of statistical experiments
60E15 Inequalities; stochastic orderings
62H20 Measures of association (correlation, canonical correlation, etc.)
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