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From |
"Naji Nassar \(MIReS\)" <naji.nassar@mires.fr> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: RE: RE: RE: Wishart distribution |

Date |
Fri, 16 Apr 2004 10:09:18 +0200 |

Dear listers Sorry if this is unrelated to Stata. > The only way you could formulate such a test would be if you have a (large) > sample of matrices. That's the case, I'll have 200 covariance matrix (simulation case, same sample size, same theoretical covariance matrix). The original data are simulated, non normal (Ramberg method), 200 simulations for each case The context : In causal modelling, ML is efficient under the hypothesis that data is multivariate normal distributed. But even when the data are not normal, covariance method is still accurate (intermediate results) in some cases and not in others. What I would like to test is whether these results are due to the covariance departure from Wishart distribution.. In Bollen book, Structural equations with latent variables, p134-135 : during estimation, ML need the multi normality in order to deal with Wishart distribution for the covariance matrix. My hypothesis (unsure whether this is can be theoretically handled): - data are not normal, but the covariance show no departure from Wishart, the ML results are accurate - data are not normal, but the covariance show significant departure from Wishart, the ML results are biased.. Best regards & thanks for your help 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 17:56 À : 'statalist@hsphsun2.harvard.edu' Objet : st: RE: RE: RE: Wishart distribution 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. 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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: RE: RE: RE: Wishart distribution***From:*"FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <alan.h.feiveson@nasa.gov>

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