Studentization and deriving accurate p-values

• 成果类型: Article
• 署名作者: Fraser, D. A. S.; Rousseau, Judith
• 署名单位: University of Toronto; Universite PSL; Universite Paris-Dauphine
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asm093
• 发表日期: 2008
• 页码: 116
• 关键词: LIKELIHOOD; inference; frequentist

摘要

We have a statistic for assessing an observed data point relative to a statistical model but find that its distribution function depends on the parameter. To obtain the corresponding p-value, we require the minimally modified statistic that is ancillary; this process is called Studentization. We use recent likelihood theory to develop a maximal third-order ancillary; this gives immediately a candidate Studentized statistic. We show that the corresponding p-value is higher-order Un(0, 1), is equivalent to a repeated bootstrap version of the initial statistic and agrees with a special Bayesian modification of the original statistic. More importantly, the modified statistic and p-value are available by Markov chain Monte Carlo simulations and, in some cases, by higher-order approximation methods. Examples, including the Behrens-Fisher problem, are given to indicate the ease and flexibility of the approach.