On a mapping approach to investigating the bootstrap accuracy

• 成果类型: Article
• 署名作者: Chen, KI; Lo, SH
• 署名单位: Columbia University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s004400050083
• 发表日期: 1997
• 页码: 197-217
• 关键词: confidence-intervals; jackknife

摘要

A simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting. It is demonstrated that the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used Edgeworth expansion approach may not be successfully applied. We then consider some examples to illustrate how this approach may be used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the Gaussian approximation. For the multivariate Kolmogorov-Smirnov statistic, we show the error of bootstrap approximation is as small as that of the Gaussian approximation. For the multivariate kernel type density estimate, we obtain an order of the bootstrap error which is smaller than the order of the error of the Gaussian approximation given in Rio (1994). We also consider an application of the bootstrap accuracy for empirical process to that for the copula process.