Asymptotics of randomly weighted u- and v-statistics: Application to bootstrap

Miklós Csörgő and Masoud M. Nasari

Journal of Multivariate Analysis, 2013, vol. 121, issue C, 176-192

Abstract: This paper is mainly concerned with asymptotic studies of weighted bootstrap for 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 more general results which we first establish for sums of randomly weighted arrays of random variables. Some of the results in this paper significantly extend some well-known results on consistency of u-statistics and also consistency of sums of arrays of random variables. We also employ a new approach to conditioning to derive a conditional central limit theorem (CLT) for weighted bootstrap u- and v-statistics, assuming the same conditions as the classical CLT for regular u- and v-statistics.

Keywords: Conditional central limit theorems; Laws of large numbers; Multinomial distribution; u- and v-statistics; Randomly weighted u- and v-statistics; Weighted arrays of random variables; Weighted bootstrap (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2013.07.008

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