Re: st: Bootstrap sampling for evaluating hypothesis tests

[Margaret MacDougall <Margaret.MacDougall@ed.ac.uk>]

Dear Maarten

Thanks for so kindly offering such a comprehensive reply. I look forward 
to exploring your suggestions.
Best wishes

Margaret

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr Margaret MacDougall
Medical Statistician and Researcher in Education
Centre for Population Health Sciences
University of Edinburgh Medical School
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E-mail:  Margaret.MacDougall@ed.ac.uk
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On 14/03/2013 10:28, Maarten Buis wrote:
> On Wed, Mar 13, 2013 at 4:04 PM, Margaret MacDougall wrote:
> > I would value receiving recommendations on literature explaining the
> > application of bootstrap sampling to assess robustness to Type I errors of a
> > proposed new hypothesis test. Better still, if the recommended references
> > contain corresponding computer syntax!
> In terms of literature references, I would look at bootstrap tests. A
> bootstrap changes the data such that the null hypothesis is true and
> looks at the proportion of replictions in which the test statistic is
> more extreme than the one observed in the original data. In bootstrap
> tests these can be used as an estimate of the p-value(*), but you can
> compare it with the asymptotic p-value returned by your tests and see
> if they correspond. It is useful to also consider the Monte Carlo
> confidence interval, which captures the variability you can expect in
> the proportion due to the fact that it is based on a random process.
> Say you find 1000 out of 20000 replications in which the test
> statistic was more extreme than the one in the original sample, than
> the Monte Carlo confidence interval can be computed by typing in
> Stata: -cii 20000 1000-
>
> If you save the p-values from all replications you can look at the
> distribution of the p-values, as I did in the examples I gave earlier.
>
> Nice introductions to bootstrap tests can be found in Chapter 4 of
> (Davison & Hinkley 1997) and Chapter 16 of (Efron & Tibshirani 1993).
> They are both good introductory texts, but I found that they
> complement one another well, so it is useful to look at both of them.
>
> You can also find more Stata code examples in the manual entry of
> -bootstrap-: Under "Remarks" go to the section titled "Achieved
> significance level", and it will give an example of how to use
> -bootstrap- to do a bootstrap test.
>
> Hope this helps,
> Maarten
>
> A.C. Davison and D.V. Hinkley (1997) Bootstrap Methods and their
> Applications. Cambridge: Cambridge University Press.
>
> B. Efron and R.J. Tibshirani (1993) An Introduction to the Bootstrap.
> Boca Raton: Chapman & Hall/CRC
>
> (*) Alternatively, for testing purposes it makes sense to use the (
> number of replictions in which the test statistic is more extreme than
> the one observed in the original data + 1 ) / ( the number of
> replications +1 ), see:  Chapter 4 of (Davison & Hinkley 1997). Though
> for a large number of replications the difference with the simple
> proportion is trivial.
>
> ---------------------------------
> Maarten L. Buis
> WZB
> Reichpietschufer 50
> 10785 Berlin
> Germany
>
> http://www.maartenbuis.nl
> ---------------------------------
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