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This paper is mainly concerned with asymptotic studies of weighted bootstrapfor u- and v-statistics. We derive the consistency of the weighted bootstrap u-and v-statistics, based on i.i.d. and non i.i.d. observations, from some moregeneral results which we first establish for sums of randomly weighted arraysof random variables. Some of the results in this paper significantly extendsome well-known results on consistency of u-statistics and also consistency ofsums of arrays of random variables. We also employ a new approach toconditioning to derive a conditional CLT for weighted bootstrap u- andv-statistics, assuming the same conditions as the classical central limittheorems for regular u- and v-statistics.

Asymptotics of Randomly Weighted u- and v-statistics: Application to Bootstrap