I recently made a question that gathered no attention: Bootstrap and numerical optimization of statistic.
I think I've come up with a much simpler and to-the-point way of asking the same thing (posted below). My question here is, can I delete the old question (it doesn't have even a comment) and create a new one, or will this be seen as me trying to game the system?
New formulation of the question
Often times the bootstrap is used with a statistic that can be analytically evaluated (both in the real and the resampled datasets), e.g. the mean.
But if the statistic can not be analytically obtained (e.g., if we are maximizing a likelihood through some numerical optimization process), each bootstrap resample will contain an "extra" degree of uncertainty, as we are not really obtaining the true statistic for each resample but an approximation to it.
Does the bootstrap account for this "extra" uncertainty?