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st: bootstrapping a regression


From   Jesper Kühl <jesper.kuhl@economics.oxford.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: bootstrapping a regression
Date   Wed, 19 Feb 2003 19:00:24 +0100

Hi STATAlisters,

I have been trying to bootstrap a regression (y=x'b+e), using "bstrap"
and "bsample" and have encounters a puzzle.

I am interested in the distributional statistics of the dependent variable
y, and and thus estimate the regression for every botstrap sample,
predict the 'bx'-part, and combine it with a random draw e* from the
distribution of estimated residuals (e_hat = y - x'b_hat) to yield the
bootstrap estimates for y, y* = b'x_hat + e*. (Hence this all goes into the
bootstrap-program caled by "bstrap")
Posting y* to "bstrap" then outputs me exactly B values (with mean, bias
and st.e. for this distrib.).
But here's my puzzle: "bstrap" draws B bootstrap samples of size N, but it
only returns me B values for y* (# of obs in the "bstrap"-output file).
Where have all the other prediction for y* gone? Following the above short
theoretical outline, it should be predicting y*-values for every observation
in all B bootstrap samples, i.e. every bootstrap sample should give a
distribution of y*s (and that's what I am looking for).

Hope some of you might be able to give me a hint!

Cheers
 Jesper

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