Nonparametric bootstrap confidence interval I have generated a 95% confidence interval $(22,25)$ for a parameter using a nonparametric bootstrapping method.  What I want to know is what value we use for the estimate of the parameter.
Is it the mean of all the bootstraps, the median of all the bootstraps, the original estimate before we bootstrapped from the original dataset, or something else?
 A: Taking the mean of your bootstrap distribution is called bagging (from bootstrap aggregating; link). I've never seen it used on parameters, just on predictions, but it has a lot in common with Bayesian model averaging, which can work well on parameters. in this framework, your parameter estimated from the original data is like your posterior mode and the bagged estimate is like your posterior mean. The posterior mean often has better accuracy out of sample, but I'm not sure that applies to your case. 
A few things to consider:


*

*Does the mean of your bootstrap distribution look like your maximum likelihood estimate? If so, it might not matter which you choose. 

*Can you try it both ways on a subset of your data and see which works better on a validation set?
A: Bootstrapping is useful for measuring the variability of sample estimates. I report my sample estimate as well as the bootstrapped confidence interval. Wikipedia appears to agree: "bootstrapping is a method for assigning measures of accuracy to sample estimates." 
A: The observed value has the highest likelihood and is usually considered to be the best estimate. Bootstrapping is a method for estimating variability, but it doesn't improve on the observed estimate of the parameter. The bootstrap estimate of the parameter should asymptote to the observed value with enough resamples...
