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Covariances of symmetric statistics. (English) Zbl 0759.62021
The author examines the second-order structure arising when a symmetric function is evaluated over intersecting subsets of random variables. The original work of W. Hoeffding [Ann. Math. Stat. 19, 293-325 (1948; Zbl 0032.04101)] on $$U$$-statistics is updated with reference to later results. New representations and inequalities are presented for covariances and applied to $$U$$-statistics.

##### MSC:
 62G99 Nonparametric inference 62J10 Analysis of variance and covariance (ANOVA) 60E15 Inequalities; stochastic orderings 62H05 Characterization and structure theory for multivariate probability distributions; copulas
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