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  • 1 Department of Economics Yale University 28 Hillhouse avenue New Haven ct 06511 USA
  • 2 Department of Probability Theory, Tashkent State Economics University Ul. Uzbekistanskaya 49, Tashkent 700098, Uzbekistan
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In this paper we prove analogues of Khintchine, 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.

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