Distribution of likelihood-based p-values under a local alternative hypothesis

• 成果类型: Article
• 署名作者: Lee, Stephen M. S.; Young, G. Alastair
• 署名单位: University of Hong Kong; Imperial College London
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw021
• 发表日期: 2016
• 页码: 641652
• 关键词: one-sided inference; nuisance parameters; models

摘要

We consider inference on a scalar parameter of interest in the presence of a nuisance parameter, using a likelihood-based statistic which is asymptotically normally distributed under the null hypothesis. Higher-order expansions are used to compare the repeated sampling distribution, under a general contiguous alternative hypothesis, of p-values calculated from the asymptotic normal approximation to the null sampling distribution of the statistic with the distribution of p-values calculated by bootstrap approximations. The results of comparisons in terms of power of different testing procedures under an alternative hypothesis are closely related to differences under the null hypothesis, specifically the extent to which testing procedures are conservative or liberal under the null. Empirical examples are given which demonstrate that higher-order asymptotic effects may be seen clearly in small-sample contexts.