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On dominations between measures of dependence. (English) Zbl 0627.60009
This paper is best summarized by the authors’ abstract: Suppose one has two measures of dependence between two or more families of random variables. One of the measures is said to “dominate” the other if the latter becomes arbitrarily small as the former becomes sufficiently small. A description is given of the entire pattern of dominations between arbitrary pairs of measures of dependence that are based on the usual norms of the bilinear form “covariance”. Also, for a broader class of measures of dependence, some earlier “domination inequalities” are shown to be essentially sharp.
Reviewer: A.Gut

MSC:
60B05 Probability measures on topological spaces
62H20 Measures of association (correlation, canonical correlation, etc.)
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