Tweedie's Formula and Selection Bias

• 成果类型: Article
• 署名作者: Efron, Bradley
• 署名单位: Stanford University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/jasa.2011.tm11181
• 发表日期: 2011
• 页码: 1602-1614
• 关键词: Empirical Bayes; winners curse; odds ratios; estimators; hypothesis; genomewide; inference; VALUES

摘要

We suppose that the statistician observes some large number of estimates z(i), each with its own unobserved expectation parameter mu(i). The largest few of the z(i)'s are likely to substantially overestimate their corresponding mu(i)'s, this being an example of selection bias, or regression to the mean. Tweedie's formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach for correcting selection bias. This article investigates its merits and limitations. In addition to the methodology, Tweedie's formula raises more general questions concerning empirical Bayes theory, discussed here as relevance and empirical Bayes information. There is a close connection between applications of the formula and James-Stein estimation.