Background: I have n samples and their average. The mean of this empirical bootstrapped distribution seems quite different form the average of my original sample. My original average for the n samples is about the 62nd percentile on the empirical distribution. It seems to me that the means should approach one another as I take more bootstrapped samples.
Questions
In general, why might the mean of a bootstrapped distribution not approach the original summary statistic as the sample size gets very large?