MATLAB: How to find the error estimates or confidence intervals for a mixed Gaussian distribution by using FIT method of GMDISTRIBUTION class in Statistics Toolbox 7.0 (R2008b)

Question

I am trying to find the error estimates or confidence intervals on the parameters generated by mixed gaussian distribution. I am trying to use the FIT method of the GMDISTRIBUTION class.

Answer 1

The ability to compute the error estimates or confidence intervals for a Gussian mixture model using GMDISTRIBUTION class is not available in the Statistics Toolbox 7.0 (R2008b).

To work around this issue, the bootstrap approach could be used to estimate the standard error. The bootstrap approach can be either nonparametric using the BOOTSTRP function or parametric by generating replicate datasets using the GMDISTRIBUTION/RANDOM method. Please refer to the following book for more details on this:

"McLachlan, G., and D. Peel, Finite Mixture Models, John Wiley & Sons, New York, 2000".

There is a caveat, the Gaussian mixture model has an identifiability problem, i.e., the likelihood does not change if one permutes the component labels. Therefore, to use the bootstrap approach one has to decide how to order the mixture components from each bootstrap iteration. To solve the problem practically, McLachlan suggests using the estimated parameter from the original data as the initial value during each bootstrap iteration. In the Statistical toolbox, this can be done by specifying the "Start' value for GMDISTRIBUTION/FIT method.