The convergence rates of the weighted bootstrap distributions for von Mises and U-statistics

Authors: Zhao, Shuran; Xu, Xingzhong; Ding, Xiaobo

Source: Journal of Nonparametric Statistics, Volume 20, Number 7, October 2008 , pp. 645-660(16)

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Abstract:

It has been proved that the weighted bootstrap method for von Mises and U-statistics provides a feasible approximation to their sample distributions. In the paper, based on a variation of the Berry-Esseen theorem for U-statistics, we further develop such first-order convergence rate under weak conditions. Moreover, in view of maximum entropy, we provide a principle to choose the weights.

Keywords: weighted bootstrap; von Mises statistics; U-statistics; Dirichlet distribution; convergence rate

Document Type: Research article

DOI: http://dx.doi.org/10.1080/10485250802280259

Affiliations: 1: Department of Mathematics, Beijing Institute of Technology, Beiging, People's Republic of China

Publication date: 2008-10-01