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

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 wei...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2012-10
Main Authors: Csorgo, Miklos, Nasari, Masoud M
Format: Article
Language:English
Subjects:
Asymptotic properties
Consistency
Random variables
Statistics
Sums
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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 CLT for weighted bootstrap u- and v-statistics, assuming the same conditions as the classical central limit theorems for regular u- and v-statistics.
ISSN:2331-8422