A quick procedure for model selection in the case of mixture of normal densities

The properties of robustness of the estimates based on the minimum integrated square error criterion can be exploited to set up a procedure in finding the number of the components of a mixture of Gaussian distributions. Each step of the procedure consists in the comparison between the estimates, according to maximum likelihood and minimum integrated square error criteria, of a mixture with a fixed number of components. The discrepancy between the two estimated densities is measured applying the concept of similarity between densities following from the Cauchy-Schwarz inequality. A test of statistical hypothesis, based on Monte Carlo significance test, is introduced to verify the similarity between the two estimates. If their similarity is rejected, the model can be changed simply adding one more component to the mixture. Numerical examples are given and main results, arising from a simulation study carried out to check the power of the procedure featuring several experimental scenarios, are provided.