Dear ALLSTAT members,
A classical example of bootstrap failure given in many text books is the following:
X~Uniform(0,theta), resampling the maximum likelihood estimator of theta, the sample maximum, gives an example of bootstrap failure, e.g. Davison and Hinkley (1997), "Bootstrap methods and their applications", page 39.
Now suppose that X~Uniform(a,b), the mean is mu=(a+b)/2 and the maximum likelihood estimator of mu is muhat=(sample minimum+sample maximum)/2.
Since it is not recommended to bootstrapping the sample maximum, can one bootstrap muhat?
If not, how to prove the bootstrap failure in this case.
Thanks in advance,
Alphonse
