# Can you infer standard deviation/error from bootstrapped confidence intervals?

I've got the summary of a data set, but not the actual data. They've calculated confidence intervals using bootstrapping. I know the sample size, so if they were normally calculated confidence intervals, I'd know how to calculate standard deviation, but is there any relationship between the size of confidence intervals calculated from bootstrapping and sd?

Also, can it be said that doubling sample size sees the width of confidence interval reduce 25%/ when they have been calculated with bootstrapping?

• The pairs bootstrap technique when used (instead of residuals bootstrap) retains the dependence structure between $\epsilon$ and $X$ so that residuals and estimates even from a non-normal distribution do not have to be corrected with heteroskedasticity-consistent (HAC) standard errors (Freedman 1981, Davison and Hinkley, 1997) – develarist Nov 29 '19 at 17:57
• Also the original question has to be read carefully. It's obvious that standard errors can be backed out of an estimated confidence interval, but the question is if standard errors can be backed out of a bootstrapped confidence interval, which usually is obtained from running $B=200$ replications on $B=200$ resampled versions of the original data – develarist Nov 29 '19 at 18:06