Information lost by conditioning on the random margins in a two-by-two table

• 成果类型: Article
• 署名作者: Schervish, M. J.; Kadane, J. B.; Seidenfeld, T.; Stern, R. B.
• 署名单位: Carnegie Mellon University; Carnegie Mellon University; Universidade de Sao Paulo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444; 1464-3510
• DOI: 10.1093/biomet/asaf064
• 发表日期: 2025
• 页码: asaf064
• 关键词: fisher information; Fraction of information lost; Partial information; EQUALITY

摘要

We study the amount of Fisher information about the odds ratio parameter that one loses by conditioning on the random margin totals of a $ 2\times 2 $ table for the cases in which the data arise either as a multinomial sample or as two independent binomial samples. When there is a nuisance parameter, as in this problem, many authors have proposed the concept of partial information to quantify the amount of Fisher information about the parameter of interest. We show that, as the sample size of the table becomes infinite (in such a way that all margin totals also become infinite), the fraction of partial information that one loses by conditioning on both margins goes to 0.