Total replicates discarded for a 90% percentile interval

Question

You generate B = 1200 bootstrap replicates and build a 90% percentile confidence interval from the 5th and 95th percentiles of the sorted replicates. In total, across both tails combined, how many replicates are discarded (fall outside the interval)?

Accepted Answer

A 90\% interval leaves \alpha = 10\% of the replicates outside, split into two equal tails of \alpha/2 = 5\% each. Per tail. 0.05 	imes 1200 = 60. Both tails combined. 60 + 60 = 120. So 120 of the 1200 replicates are discarded and the middle 1080 (that is 90\%) form the interval. Takeaway. The total trimmed for a percentile interval is \alpha 	imes B; here 10\% of 1200 is 120, split 60 per side.

Total replicates discarded for a 90% percentile interval

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