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Bounds on moments of symmetric statistics. (English) Zbl 1064.60031
Summary: We prove analogues of Khinchin, Marcinkiewicz-Zygmund and Rosenthal moment inequalities for symmetric statistics of arbitrary order in not identically distributed random variables. We also construct an example that shows the significance of each term in the obtained Rosenthal-type inequalities for symmetric statistics and obtain results concerning the rate of growth of the best constants in the inequalities.

MSC:
60E15 Inequalities; stochastic orderings
60F25 \(L^p\)-limit theorems
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