Which ranked replicate is the lower endpoint of a 99% CI?

Question

You run B = 3000 bootstrap replicates and sort them from smallest to largest to build a 99% percentile confidence interval (the 0.5th and 99.5th percentiles). Counting from the bottom, which ranked replicate marks the lower endpoint of the interval?

Accepted Answer

A 99\% interval leaves \alpha = 1\% outside, split into two tails of \alpha/2 = 0.5\% each. The lower endpoint sits at the 0.5\% point of the sorted replicates. Rank of the lower endpoint. \frac{\alpha}{2} 	imes B = 0.005 	imes 3000 = 15. So the lower endpoint is the 15th-smallest replicate (and by symmetry the upper endpoint is the 15th-largest, i.e. the 2985th). Tighter confidence means trimming fewer replicates from each tail, pushing the endpoints further out into the extremes. Takeaway. The lower endpoint of a percentile interval sits at rank (\alpha/2)	imes B from the bottom; for 99\…

Which ranked replicate is the lower endpoint of a 99% CI?

Your answer

Discussion

Learn the concepts

Related questions