**Question 1**What estimator should be used ?**Question 2**Having chosen an estimator, how accurate is it ?

The second question has to be answered through information on the distribution or at least the variance of the estimator.

Of course there are answers in very simple contexts:
for instance when the parameter of interest is
the mean then the estimator
has a known standard
deviation : the estimated standard error
noted sometimes

However no such estimator is available for the sample median for instance.

In maximum likelihood theory the question 1 is answered through using the mle and then the question 2 can be answered with an approximate standard error of

The bootstrap is a more general way to answer question 2 , with the following aspects:

- Less or no parametric modelling.
- More computation. (a factor 100 to 1000)
- Automatic, whatever the situation (can be complex).

If we had several samples from the unknown
(true) distribution
then we could consider the variations
of the estimator :

Such a situation is never the case, so we replace these new samples by a resampling procedure based on the only information we have about , and that is an empirical :this side is what is called