Moments of randomly stopped $U$-statistics
de la Peña, Victor H. ; Lai, Tze Leung
Ann. Probab., Tome 25 (1997) no. 4, p. 2055-2081 / Harvested from Project Euclid
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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.
Publié le : 1997-10-14
Classification:  Decoupling inequalities,  martingales,  stopping times,  $U$-statistics,  Wald’s equation,  uniform integrability,  60G40,  60F25,  62L12 
@article{1023481120,
     author = {de la Pe\~na, Victor H. and Lai, Tze Leung},
     title = {Moments of randomly stopped $U$-statistics},
     journal = {Ann. Probab.},
     volume = {25},
     number = {4},
     year = {1997},
     pages = { 2055-2081},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1023481120}
}

de la Peña, Victor H.; Lai, Tze Leung. Moments of randomly stopped $U$-statistics. Ann. Probab., Tome 25 (1997) no. 4, pp.  2055-2081. http://gdmltest.u-ga.fr/item/1023481120/