On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.