Adaptive multigroup confidence intervals with constant coverage

• 成果类型: Article
• 署名作者: Yu, C.; Hoff, P. D.
• 署名单位: University of Washington; University of Washington Seattle; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy009
• 发表日期: 2018
• 页码: 319335
• 关键词: prior information; sets; parameters; variances

摘要

Commonly used interval procedures for multigroup data attain their nominal coverage rates across a population of groups on average, but their actual coverage rate for a given group will be above or below the nominal rate, depending on the group mean. While correct coverage for a given group can be achieved with a standard t-interval, this approach is not adaptive to the available information about the distribution of group-specific means. In this article we construct confidence intervals that have a constant frequentist coverage rate and that make use of information about across-group heterogeneity, resulting in constant-coverage intervals that are narrower than standard t-intervals on average across groups. Such intervals are constructed by inverting biased Bayes-optimal tests for the mean of each group, where the prior distribution for a given group is estimated with data from the other groups.