Moment Inequalities for Symmetric Statistics
R. Ibragimov, Sh. Sharakhmetov
TL;DR
This paper extends classical moment inequalities to symmetric statistics of any order, providing new bounds and demonstrating their significance through examples.
Contribution
It introduces analogues of Khintchine and Rosenthal inequalities for symmetric statistics of arbitrary order, with illustrative examples.
Findings
Established new moment inequalities for symmetric statistics
Constructed examples demonstrating the importance of each term in the bounds
Extended classical inequalities to higher-order symmetric statistics
Abstract
In this paper, we prove analogues of Khintchine and Rosenthal's moment inequalities for symmetric statistics (U-statistics) of arbitrary order. An example that shows significance of each term in the analogues of Rosenthal's bounds for symmetric statistics is constructed as well.
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Taxonomy
TopicsStatistical Distribution Estimation and Applications · Statistical Methods and Inference · Advanced Statistical Methods and Models