ON THE EDGEWORTH EXPANSION AND THE BOOTSTRAP APPROXIMATION FOR A STUDENTIZED U-STATISTIC

• 成果类型: Article
• 署名作者: HELMERS, R
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176347994
• 发表日期: 1991
• 页码: 470-484
• 关键词: confidence-intervals; jackknife

摘要

The asymptotic accuracy of the estimated one-term Edgeworth expansion and the bootstrap approximation for a Studentized U-statistic is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of a Studentized U-statistic than the normal approximation. The conditions needed to obtain these results are weak moment assumptions on the kernel h of the U-statistic and a nonlattice condition for the distribution of g(X1) = E[h(X1, X2)\X1]. As an application improved Edgeworth and bootstrap based confidence intervals for the mean of a U-statistic are obtained.