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st: Re: Bootstrapping prediction standard error


From   Richard Sperling <rsperling@rcn.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: Bootstrapping prediction standard error
Date   Fri, 24 Aug 2007 07:02:48 -0400

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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