Conditional properties of unconditional parametric bootstrap procedures for inference in exponential families

• 成果类型: Article
• 署名作者: Diciccio, Thomas J.; Young, Alastair
• 署名单位: Cornell University; Imperial College London
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asn011
• 发表日期: 2008
• 页码: 747758
• 关键词: log likelihood ratio; gamma-distribution; shape parameter; tests

摘要

Higher-order inference about a scalar parameter in the presence of nuisance parameters can be achieved by bootstrapping, in circumstances where the parameter of interest is a component of the canonical parameter in a full exponential family. The optimal test, which is approximated, is a conditional one based on conditioning on the sufficient statistic for the nuisance parameter. A bootstrap procedure that ignores the conditioning is shown to have desirable conditional properties in providing third-order relative accuracy in approximation of p-values associated with the optimal test, in both continuous and discrete models. The bootstrap approach is equivalent to third-order analytical approaches, and is demonstrated in a number of examples to give very accurate approximations even for very small sample sizes.