Dear list,
I posted a question on August 16 with the subject "Bootstrapping
prediction standard error." To the best of my knowledge, I did not
receive a reply. I also sent the question to a statistician I know.
He replied with what I believe is a solution to the problem.
I am not going to repeat my question as it was long. In any event,
you can find my original post in the Statalist archives.
I want to bootstrap the standard error of the prediction for the
functional form y = (a + b*x^g) * e, e ~ N(1,\sigma^2). Previously,
my statistics friend believes I had been bootstrapping the standard
error of the regression rather than the standard error of the
prediction.
The functional form is the product of two random variables, y = z*e,
where z = a + b*x^g. So I can use the bootstrap to estimate the
variance of z and the variance of the error, e. Then I can follow
Goodman (1960) (http://www.jstor.org/view/01621459/
di985863/98p04677/0) to calculate the exact variance of a product of
random variables. My colleague also notes that "[i]f you want to
compute a prediction interval, then your distributional assumptions
will come into play."
I hope this information may be helpful to someone in the future.
Richard Sperling
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