General ways to improve FCR-adjusted selective confidence intervals
Abstract Recently, post-selection inference on thousands of parameters has attracted considerable research interest. 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. Although Benjamini-Yekutieli’s confidence intervals are widely used, they are uniformly inflated. In this article, two methods are proposed to narrow Benjamini-Yekutieli’s confidence intervals. The first method improves the confidence intervals by incorporating the selection event into the calculation. The second method further narrows 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 analyzed to compare the methods.