General ways to improve false coverage rate-adjusted selective confidence intervals. (16th February 2021)

• Record Type: Journal Article
• Authors: Zhao, Haibing
• Is Part Of: Biometrika. Volume 109:Number 1(2022)
• Page Start: 153
• Page End: 164
• Publication Date: 2021-02-16
• Subjects: False coverage rate -- Post-selection -- Selective confidence interval -- Simple thresholding selection; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asab010
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: 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.