Abstract
In this paper we provide sharp bounds on the $L_p$-norms of randomly stopped $U$-statistics. These bounds consist mainly of decoupling inequalities designed to reduce the level of dependence between the $U$-statistics and the stopping time involved. We apply our results to obtain Wald’s equation for $U$-statistics, moment convergence theorems and asymptotic expansions for the moments of randomly stopped $U$-statistics. The proofs are based on decoupling inequalities, symmetrization techniques, the use of subsequences and induction arguments.
Citation
Tze Leung Lai. Victor H. de la Peña. "Moments of randomly stopped $U$-statistics." Ann. Probab. 25 (4) 2055 - 2081, October 1997. https://doi.org/10.1214/aop/1023481120
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