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Re: st: bootstrap and XTIVREG2


From   "Stas Kolenikov" <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: bootstrap and XTIVREG2
Date   Sat, 15 Sep 2007 09:36:35 -0500

On 9/14/07, Erasmo Giambona <e.giambona@gmail.com> wrote:
> Dear Stas,
> As you expected most of my results are unchanged. However, one of the
> variable looses significance. The number of cluster that I have is
> quite large (about 1600). Can it be bootstrapping is eliminating the
> effect of some outliers?

Well if anything bootstrap amplifies the outliers. Think about say
inference on a sample mean of 9 values from uniform (0,1), and one
sample value equal to 10. Then in 35% (=0.9^10) the outlier will be
absent, and the mean will be around 0.5; in some 38%=(10 choose 1 *
0.9^9 * 0.1), it will be present once, so that the mean will be around
1.5; and in the remaining cases, the outlier will be resampled twice
or more often, so you'll see the mean of some 2.5 or more. Out of blue
sky, you've got a distribution with multiple modes, which may not be
very close to the true distribution of the mean even if the original
distribution was heavy tailed, as the distribution of the mean would
probably be reasonably smooth. Also, the normal approximation for this
distribution will be terrible, and 1.96 magic number won't work to
give you the tail 5%. You could look into the -estat bootstrap- after
all, to see how your confidence interval are doing, as that's where
the bootstrap really gets an edge against symmetric things like the
sandwich standard errors.

Besides you would need to remember that anything you get out of sample
is subject to sampling fluctuations and type I/II/III errors. If your
variable was borderline with p-value of 3% with the sandwich standard
errors, and now borderline 7% with the bootstrap standard errors, I
wouldn't bother.

To Austin: I am reading the wild cluster bootstrap paper, looks
interesting, although I will suggest another 15 or so references to
the authors :)).

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: Please do not reply to my Gmail address as I don't check
it regularly.
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