Calibrating and Visualizing Some Bootstrap Confidence Regions

Abstract

When the bootstrap sample size is moderate, bootstrap confidence regions tend to have undercoverage. Improving the coverage is known as calibrating the confidence region. Consider testing H0:θ=θ0 versus H1:θ≠θ0. We reject H0 only if θ0 is not contained in a large-sample 95% confidence region. If the confidence region has 3% undercoverage for the data set sample size, then the type I error is 8% instead of the nominal 5%. Hence, calibrating confidence regions is also useful for testing hypotheses. Several bootstrap confidence regions are also prediction regions for a future value of a bootstrap statistic. A new bootstrap confidence region uses a simple prediction region calibration technique to improve the coverage. The DD plot for visualizing prediction regions can also be used to visualize some bootstrap confidence regions.

Keywords

• data splitting
• prediction regions