Accurate and efficient double-bootstrap confidence limit method
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TL;DR
It turns out that the double-bootstrap confidence limit method modifies the percentile method by taking the [(B+1)β]th smallest value with β estimated through an efficient double- bootstrap equation is accurate in general and exact for the mean of both Normal and Exponential distributions under parametric bootstrap.
Abstract
Abstract The original percentile method takes the [(B + 1)α]th smallest value among B bootstrapped ĝq∗'s as an upper 100α% confidence limit for θ. The double-bootstrap confidence limit method modifies the percentile method by taking the [(B+1)β]th smallest value with β estimated through an efficient double-bootstrap equation. It turns out that the method is accurate in general, and exact for the mean of both Normal and Exponential distributions under parametric bootstrap.