Certain Uncorrelated and Independent Rank Statistics

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Abstract
Some interesting examples of uncorrelated simple linear rank statistics are listed. Consideration is then given to conditions under which general rank statistics are uncorrelated or have joint distributions which enjoy certain symmetric properties. Two simple linear rank statistics that are uncorrelated are found, under suitable restrictions, to be asymptotically independent. This is followed by some illustrations in which two rank statistics are exactly independent. The importance of these results about independence in actual testing is then noted.

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