General ways to improve false coverage rate-adjusted selective confidence intervals

• 成果类型: Article
• 署名作者: Zhao, Haibing
• 署名单位: Shanghai University of Finance & Economics
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab010
• 发表日期: 2022
• 页码: 153164
• 关键词: Empirical Bayes

摘要

Post-selection inference on thousands of parameters has attracted considerable research interest in recent years. Specifically, Benjamini & Yekutieli (2005) considered constructing confidence intervals after selection. They proposed adjusting the confidence levels of marginal confidence intervals for the selected parameters to ensure control of the false coverage-statement rate. However, although Benjamini-Yekutieli confidence intervals are widely used, they are uniformly inflated. In this article, two methods for narrowing the Benjamini-Yekutieli confidence intervals are proposed. The first improves the confidence intervals by incorporating the selection event into the calculation. The second method further narrows those confidence intervals in which some parameters are selected with very small probabilities, which results in underutilization of the target level for control of the false coverage-statement rate. A breast cancer dataset is analysed to compare the methods.