Journal
BIOMETRIKA
Volume 109, Issue 1, Pages 153-164Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/asab010
Keywords
False coverage rate; Post-selection; Selective confidence interval; Simple thresholding selection
Funding
- National Natural Science Foundation of China
- Fundamental Research Funds for the Central Universities
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Post-selection inference on thousands of parameters has been studied in recent years. This article proposes two methods for narrowing the confidence intervals, by incorporating the selection event into the calculation and focusing on parameters with very small selection probabilities.
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.
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