# Monte Carlo variation in bootstrapping?

I am obtaining confidence intervals using different bootstrap methods. When comparing them, what is does it mean to use Monte Carlo variation to look at how much the upper and lower limits vary for each bootstrap?

• It sounds like you are quoting something. Could you provide a reference or link to the source?
– whuber
Apr 5, 2012 at 19:04
• Its a homework question. I have to test the performance of bootstrapping methods for confidence intervals. The Monte Carlo variation was a suggestion on how to do this. Apr 5, 2012 at 19:16
• The problem is that "Monte Carlo variation" could mean a few different things, such as a distribution of a resampling statistic or the variation due to the fact that many bootstrapped estimates are approximations made by means of Monte-Carlo sampling and are thereby subject to sampling variation. Some more context would be helpful. If it's homework for a course having a real live teacher, consider consulting them about the intended meaning.
– whuber
Apr 5, 2012 at 19:18
• Ok, I think it means that they are subject to variation. Is working out the variance the same as looking at how much the confidence limits vary for each simulation in the bootstrap? Apr 5, 2012 at 19:48
• This is a well written paper on this topic: On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses (Koehler, Brown, Haneuse) amstat.tandfonline.com/doi/abs/10.1198/… Apr 5, 2012 at 20:57