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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?

Jeromy Anglim
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Alex Charl
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    It's hard to guess what's going wrong from such an abstract general statement. Could you provide some details of what you've done? – whuber Mar 27 '13 at 20:04
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    It is possible this question may be asking about phenomena like that illustrated at http://stats.stackexchange.com/questions/62899/how-to-calculate-confidence-intervals-for-power-function-y-axb-in-r-using-n/63169#63169, where bootstrapping reveals the inherent bias in an estimator. (This was one of the original motivations of the bootstrap, to find a way to estimate the bias in an estimator.) Taking more bootstrapped samples merely improves the precision with which that bias is computed. – whuber Jul 07 '13 at 15:14

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