How many bootstrap replicates land inside a 95% interval?

Question

You run B = 8000 bootstrap replicates and build a 95% percentile confidence interval from the 2.5th and 97.5th percentiles. How many of the sorted replicates fall inside the interval (between the two endpoints)?

Accepted Answer

A percentile interval at level 95\% keeps the middle 95\% of the replicates, discarding \alpha/2 = 2.5\% from each tail. Replicates inside the band. (1 - \alpha) 	imes B = 0.95 	imes 8000 = 7600. The remaining 400 are trimmed, 200 off each tail. Increasing B does not change these fractions; it just makes the endpoints (the empirical quantiles) more stable. Takeaway. A 95\% percentile interval holds the central 1-\alpha = 95\% of replicates; with B = 8000 that is 7600 of them.

How many bootstrap replicates land inside a 95% interval?

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