Re: st: joint hypothesis test with one sided alternatives

[Stas Kolenikov <skolenik@gmail.com>]

Na-ah, it's not going to work. You need to bootstrap under the null
hypothesis to achieve this end. And to bootstrap under the null, you
need to transform your data, which is rarely entirely convincing. In
this case, it would look like

regress Y X1 X2
predict e, res
bootstrap : regress e X1 X2

and then you can count the number of times the coefficients are in the
quadrant of interest, etc.

There's literature on estimation when the true parameter is on the
boundary of the parameter space, and the alternatives are one-sided
(see http://www.citeulike.org/user/ctacmo/tag/boundary). You will have
a crazy mixture of chi-squares as the reference distribution. You can
get the weights of the components of that mixture from the information
matrix, (X'X)^{-1}

On Wed, Mar 9, 2011 at 12:55 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> Seems that you could (should?) bootstrap the fraction of times your inequalities are both satisfied.
>
> Note that if a1 < 0 and a2 > 0 then a1 * a2 < 0 so you need to look at the inequalities separately.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Andreas Drichoutis
>
> Thanks for the reply.
>
> test does not allow to test inequalities i.e., it only displays two-sided
> tests.
>
> Any other solutions?
>
> Muyang Zhang
>
> They are not equivalent. You can simply use -test- with multiple
> equations/inequalities.
>
> 2011/3/9 Andreas Drichoutis <adrihout@cc.uoi.gr>:
>
>> I estimate an interval regression model of the form Y=_cons+a1*X1+a2*X2 .
>>
>> How would I run a joint hypothesis test with one sided alternatives e.g.
>> that a1>0 & a2<0.
>>
>> Is this equivalent to testing a1*a2<0 ? Is it valid to use?:
>> testnl _b[a1]*_b[a2]=0
>> local sign_test=sign(_b[a1]*_b[a2])
>> di _b[a1]*_b[a2] "   H0: coef<0 p-value= "
>> 1-normal(`sign_test'*sqrt(r(chi2)))
>
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-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
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