# Shifting bootstrap confidence interval to be centered around original parameter

I've been doing a bit of research into bootstrapping as I've been told one method of performing it, and this seems to differ from what I can find in other sources.

I have a sample, and want to estimate the mean or median. I generate 1000 resamples, without replacement, calculating the mean/median for each. By taking the 26th largest and 26th smallest mean/median I calculate, I get a confidence interval.

The sources I've read seem to leave it at that. However, the method I was told went one step further - it calculates the width of this interval, then generates a new interval that is centered around the mean/median of my original sample.

So, if my original mean was 20, and bootstrapping gives me an interval of [17,27], it shifts this to give a final confidence interval of [15,25].

Does this make sense / have any statistical backing? Or is this a mistake?

• You should not be too worried about the symmetry of the interval but about its coverage properties. Asymmetry of the Bootstrap distribution is common when the sample size (of the original distribution) is small/medium. Please, have a look at this paper about the construction of several types of Bootstrap confidence intervals. The ones you are constructing are sort of "quantile-type" CI, but it is better to calculate, say, the $0.025$ and $0.975$ empirical quantiles and construct the corresponding 95% interval.
– user10525
Jun 14, 2012 at 7:32