st: bootstrapping question

["a.carrozzone@libero.it" <a.carrozzone@libero.it>]

Dear Statalist,

I have a basic question on bootstrapping.

I need to test the hypothesis that a statistic, X, has mean equal to zero.

I can obtain the standard deviation of X, SE, across the bootstrapping 
replications. Following the traditional approach, I can use SE as the standard 
error of X. And, if I assume that X is asymptotically normally distributed, 
X/SE is asymptotically distributed as a standard normal. Accordingly, Stata 
computes the z-statistic.

However, if I don’t know the asymptotic distribution of X, how can I compute 
the critical values of the test statistic X/SE?

Another question: would it make sense instead to run a t-test on the series of 
estimated X obtained with bootstrap?
 
Thanks  a lot,


Andrea

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