Mark Schaffer
> I've just discovered that -estimates post-
> in version 7
> seems to behave inconsistently when the covariance matrix
> being posted is
> not positive definite. Sometimes it posts the matrix
> without complaint;
> other times it bombs out with error 506, "matrix not
> positive definite". A
> demonsration is below.
>
> Any ideas about why -est post- might accept some non-pd
> matrices and not
> others?
>
> --Mark
>
> * This covariance matrix is not positive definite,
> * and -est post- will refuse to post it.
>
> . mat list Vsave
>
> symmetric Vsave[4,4]
> L.
> p w p _cons
> p .00649023
> w -.00412379 .001033
> L.p -.00480518 .00311278 .00541914
> _cons .15565638 -.03696101 -.14100874 1.592022
>
> . mat list bsave
>
> bsave[1,4]
> L.
> p w p _cons
> y1 .19293435 .79621877 .08988469 16.236603
>
> . matsqrt Vsave
> matrix is not poisitive definite
> r(504);
>
> . est post bsave Vsave
> matrix not positive definite
> r(506);
>
> * This matrix covariance matrix is also not positive definite,
> * but -estimates post- will post it anyway.
>
> . mat list Vsave2
>
> symmetric Vsave2[4,4]
> L.
> p w p _cons
> p .02953177
> w -.0035374 .00122606
> L.p -.02182449 .00140922 .01935147
> _cons -.01117901 -.02100185 .0169305 1.0082315
>
> . mat list bsave2
>
> bsave2[1,4]
> L.
> p w p _cons
> y1 .01730217 .81018271 .21623384 16.554759
>
> . matsqrt Vsave
> matrix is not poisitive definite
> r(504);
>
> . est post bsave2 Vsave2
>
> . mat list e(V)
>
> symmetric e(V)[4,4]
> L.
> p w p _cons
> p .02953177
> w -.0035374 .00122606
> L.p -.02182449 .00140922 .01935147
> _cons -.01117901 -.02100185 .0169305 1.0082315
>
Here's a guess: this is a replay, with details changed,
of the "when is a matrix (deemed to be) symmetric?" debate
(see e.g. Vince Wiggins' 10 June posting on that, also
to Mark).
In principle, a matrix is positive definite or not,
period, as every pure mathematician will (presumably) insist.
Write a program to do it, using finite precision arithmetic
etc., and things are not quite so straightforward,
as every numerical analyst will (presumably) insist.
Mark is using -matsqrt-, as a test, but is this
doing ___exactly____ the same thing?
Nick
[email protected]
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