How many bootstrap replicates get trimmed for a percentile CI?

Question

You run B = 2000 bootstrap replicates of a statistic, sort them, and build a 95% percentile confidence interval by taking the 2.5th and 97.5th percentiles as the endpoints. How many of the sorted replicates are trimmed off in each tail (below the lower endpoint, and above the upper endpoint)?

Accepted Answer

The percentile method keeps the middle chunk of the sorted bootstrap replicates and throws away a slice from each end. For a 95\% interval, the two tails together hold \alpha = 5\% of the replicates, split evenly, so each tail holds \alpha / 2 = 2.5\%. Per-tail count. \frac{\alpha}{2} 	imes B = 0.025 	imes 2000 = 50. So 50 replicates sit below the lower endpoint and 50 sit above the upper endpoint, leaving the middle 1900 (that is 95\%) inside the interval. The lower endpoint is essentially the 50th-smallest replicate and the upper endpoint the 50th-largest. Takeaway. A percentile interval …

How many bootstrap replicates get trimmed for a percentile CI?

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