Sometimes in a paper I see that (e.g.) confidence intervals were estimated using 99 (or 199 or 999) bootstraps. My question is, why 99 rather than 100?
This is my best guess at an answer:
"If we sort the results from 100 bootstraps, the 5th and 95th results are estimates of the 5th and 95th percentiles of the whole population, which would give us a 90% confidence interval. But the estimator only converges as sample size goes to infinity. With a finite sample, the estimator will be inaccurate, and half the time we will get a too narrow confidence interval. Taking 99 bootstraps, the 5th and 95th results are conservative estimates of the population percentiles. For reasonable sample sizes, they are pretty sure to cover the true interval between 5th and 95th population percentiles."
Is that right, or close?