NORMALIZING TRANSFORMATIONS AND BOOTSTRAP CONFIDENCE-INTERVALS

• 成果类型: Article
• 署名作者: KONISHI, S
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348393
• 发表日期: 1991
• 页码: 2209-2225
• 关键词: edgeworth expansion; jackknife; approximations; statistics

摘要

This paper considers the problem of constructing approximate confidence intervals for functional parameters in the nonparametric case. The approach based on transformation theory is applied to improve standard confidence intervals. The accelerated bias-corrected percentile interval introduced by Efron relies on the existence of a normalizing transformation with bias and skewness corrections, although calculation does not require explicit knowledge of its functional form. We formally construct such a transformation and estimate bias and skewness correction factors for nonparametric situations. The resulting interval is shown to be second-order accurate. To this end Edgeworth expansions for the distributions of transformed statistics are derived, using the von Mises expansion.