The multivariate polykays, or multipart k-statistics, are obtained as a slight extension of results given by Tukey [4] for the univariate polykays. The relationship between this system and the system of multivariate symmetric means is indicated and multiplication formulas are given. An application of these results to the construction of unbiased ratio-type estimators and variance estimates for finite populations is given as a further illustration of the usefulness of polykays.
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D. S. Robson (1957) studied this question.
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