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From: Hydra on 8 Mar 2010 21:56
The description in documentation for gmdistribution states:

The Akaike Information Criterion: 2*NlogL+2*m, where m is the number of estimated parameters.

What does Matlab use for m? My interpretation would be nComponents*[nDimensions*(1+nDimensions)] because both the algorithm is estimating the means and covariances.

Anyone know for sure?

Peter Perkins <Peter.Perkins(a)MathRemoveThisWorks.com> wrote in message <gqt554$gj2$2(a)fred.mathworks.com>...
> sneha wrote:
> > Hi all,
> >
> > Thank you for the response, Actually I went through the
> > gmdistribution i am unable to follow AIC and BIC functions can any
> > one plz.. help me redg.. Input that are required,in bit detail
> > particualarly of garch.... instruction
>
> sneha, I suggest you look at the documentation for the GMDISTRIBUTION class:
>
> <http://www.mathworks.com/access/helpdesk/help/toolbox/stats/index.html?/access/helpdesk/help/toolbox/stats/gmdistributionclass.html>
From: Peter Perkins on 9 Mar 2010 06:48
On 3/8/2010 9:56 PM, Hydra wrote:
> The description in documentation for gmdistribution states:
>
> The Akaike Information Criterion: 2*NlogL+2*m, where m is the number of
> estimated parameters.
>
> What does Matlab use for m? My interpretation would be
> nComponents*[nDimensions*(1+nDimensions)] because both the algorithm is
> estimating the means and covariances.

Except that the cov matrix is symmetric, and might be diagonal, and might be shared.

The code is the easiest place to look. Edit gmdistribution/fit, search for AIC, and you will find that nParams depends on the chosen covariance model. In the case where the cov matrices are fully parameterized, and separately estimated for each component, there are

k-1 mixing probabilities
k*ndims means
k*ndims*(ndims+1)/2 covariances

parameters estimated.

From: Hydra on 9 Mar 2010 09:15
Thanks. I was shooting from the hip and had forgotten about weights, symmetry, and options!

Peter Perkins <Peter.Perkins(a)MathRemoveThisWorks.com> wrote in message <hn5cit$n36$1(a)fred.mathworks.com>...
> On 3/8/2010 9:56 PM, Hydra wrote:
> > The description in documentation for gmdistribution states:
> >
> > The Akaike Information Criterion: 2*NlogL+2*m, where m is the number of
> > estimated parameters.
> >
> > What does Matlab use for m? My interpretation would be
> > nComponents*[nDimensions*(1+nDimensions)] because both the algorithm is
> > estimating the means and covariances.
>
> Except that the cov matrix is symmetric, and might be diagonal, and might be shared.
>
> The code is the easiest place to look. Edit gmdistribution/fit, search for AIC, and you will find that nParams depends on the chosen covariance model. In the case where the cov matrices are fully parameterized, and separately estimated for each component, there are
>
> k-1 mixing probabilities
> k*ndims means
> k*ndims*(ndims+1)/2 covariances
>
> parameters estimated.
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