RE: st: joint hypothesis test with one sided alternatives

[Nick Cox <n.j.cox@durham.ac.uk>]

I mean that you cannot collapse the two inequalities into one, as you suggested in your first posting, as the product will be negative if precisely one term is positive and the other is negative. This is just elementary algebra. 

The deeper statistical point is that -test-, as you say, does not address your problem. Therefore another approach is to count how many times your inequalities are jointly satisfied as you shuffle the data, e.g. with a bootstrap. 

Nick 
n.j.cox@durham.ac.uk 

Andreas Drichoutis

Can you be more specific? Why do I need to look at the inequalities
separately? Is a separate test valid?

I also tried bootstrapping: 	bootstrap ((_b[a1]<0)&(_b[a2]>0)): intreg
left right x1 x2 

But I get the below output:

----------------------------------------------------------------------------
--
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
       _bs_1 |  (dropped)
----------------------------------------------------------------------------
--


Nick Cox

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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