Re: st: Bootstrap sampling for evaluating hypothesis tests

[Maarten Buis <maartenlbuis@gmail.com>]

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!

Rich Williams and I are currently working on such a project. In
general I would not say that a test is "robust" against Type I errors
but that the Type I error rate corresponds to your prespecified level
of significance. Type I errors will occur, but the chance of it
occuring should be the same as the level of significance you have
chosen. This means that if we change the data such that the null
hypothesis is true and bootstrap from that changed dataset the
p-values should follow a uniform distribution. This changing the data
is inevitable when assessing the Type I error rate: in order to assess
the probability of rejecting a true null hypothesis you first need to
make sure that the null hypothesis is true.

Here are two examples of how to do this in Stata:

*------------------ begin example ------------------
clear all
sysuse auto
recode rep78 1/2=3
logit foreign price
predict double pr
gen byte ysim = .
keep foreign price rep78 pr ysim
keep if !missing(foreign,price,rep78)
program define sim
	replace ysim = runiform() < pr
	logit ysim  price ib3.rep78
	test 4.rep78 = 5.rep78 = 0
end
simulate chi2=r(chi2) p=r(p), reps(1000) : sim
simpplot p
qchi chi2, df(2) name(q)
*------------------- end example -------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

*------------------ begin example ------------------
clear all
sysuse auto
gen lnprice = ln(price)
reg turn mpg i.rep78 foreign
predict double mu1

reg turn mpg i.rep78 foreign weight lnprice
predict double mu2
gen double ysim = turn - mu2 + mu1

keep ysim mpg rep78 foreign weight lnprice
keep if !missing(ysim, lnprice, mpg, rep78, foreign, weight)
tempfile temp
save `temp'

 program define qenv_sim_F
    use `1', clear
    bsample
    reg ysim mpg i.rep78 foreign weight lnprice
    test weight lnprice
end

simulate F=r(F) p=r(p), reps(1000): qenv_sim_F `temp'

simpplot p
*------------------- end example -------------------
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )

Hope this helps,
Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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