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st: RE: RE: RE: Wishart distribution


From   "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <alan.h.feiveson@nasa.gov>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: RE: RE: Wishart distribution
Date   Thu, 15 Apr 2004 10:55:34 -0500

Naji - If you have only one such matrix, the answer is that as long as the
matrix is symmetric and positive definite or semi-definite, there is no
test. This is because any symmettirc positive matrix could arise as a sample
of one from some legitimate Wishart distribution.

To see this, suppose you had only one dimension. Then your matrix would be
some number, say 64.5.Your question would be equivalent to asking whether
64.5 could have been generated by sig^2 times a chi-squared random variable
divided by its degress of freedom. The answer, of course is "yes", since
there is always a value of sig^2 that will work.

The only way you could formulate such a test would be if you have a (large)
sample of matrices.

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Naji Nassar
(MIReS)
Sent: Thursday, April 15, 2004 9:34 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: RE: Wishart distribution


Hi Al,


- How can I test whether an observed covariance (from a sample size) follow
the theoretical distribution?
As input, I have the observed covariance matrix (pxp) and sample size (n)
(not the original data) and the theoretical covariance matrix (pxp).

Best
Naji

-----Message d'origine-----
De : owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]De la part de FEIVESON,
ALAN H. (AL) (JSC-SK) (NASA)
Envoyé : jeudi 15 avril 2004 15:08
À : 'statalist@hsphsun2.harvard.edu'
Objet : st: RE: Wishart distribution


Naji - I assume that all you have is S, not the original data - otherwise
you could test if the original data is distributed as multivariate Normal.
Is this the case?
Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Naji Nassar
(MIReS)
Sent: Thursday, April 15, 2004 7:34 AM
To: statalist@hsphsun2.harvard.edu
Subject: st: Wishart distribution


Hi all,

Some question about covariance matrix and Wishart dist.
I've a theorical covariance matrix S.
Suppose X RandomNormal(N,p)*CholDecomposition(S) a random correlated
variable.
- What is the theoretical distribution of X covariance (Wishart(S,nobs)?)
- How can I test whether an observed covariance (from a sample size) follow
the theoretical distribution.

Thanks & Best Regards
Naji


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