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Re: st: Test Joint Hypothesis of several Inequalities?

From   Stas Kolenikov <>
Subject   Re: st: Test Joint Hypothesis of several Inequalities?
Date   Sat, 4 Dec 2010 09:10:11 -0600

Your hypothesis space does not cover the whole of reals^5, but only
the opposite sectors with all positive and all negative values. Your
current situation with some positive and some negative estimates falls
into neither the null nor the alternative you specified.

You might want to check Silvapulle & Sen's book on constrained
inference. They cover this stuff in all the details. What you describe
below is not making much sense, although it resembles the ultimate
result of a test with an inequality-constrained parameter.

On Sat, Dec 4, 2010 at 7:47 AM, Jen Zhen <> wrote:
> Dear Listers,
> I have run -reg outcome D1 D2 D3 D4 D5- and would like to test the
> hypothesis that all 5 dummies have a negative coefficient.
> In the regression output I find that some have positive and some
> negative signs, and none is statistically significant on its own,
> after controlling for the others.
> Now I'm wondering how I could best test my hypothesis that "D1<0 &
> D2<0 & D3<0 & D4<0 & D5<0", or test the alternative that each of them
> is >=0.
> I understand previous list entries as saying that I should test the
> Null that a coefficient is zero, and then reject my true Null if
> either the sign is wrong or the p-value of the 0 Null divided by 2 is
> still in excess of 1 minus my desired confidence level?
> But how would I test a joint hypothesis comprising several inequalities?
> Thanks a lot,
> JZ
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Stas Kolenikov, also found at
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