# st: RE: RE: RE: Wishart distribution

 From "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" To "'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
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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