In many modeling situations, we often have a choiche. We can add to model complexity to describe some unusual observations or groups of observations or we can remove those observations and fit the rest with a different, perhaps simpler, model. Purpose of this work is to illustrate a procedure in finding the number of the components of a mixture of bivariate normal densities, exploiting in this way the properties of robustness of the estimates based on the Minimum Integrated Squared Error (or Minimum L_2 distance). Each step of the procedure consists in the comparison between the estimates of the parameters of the mixture according to the Maximum Likelihood and Minimum $L_2$ distance criteria. If their difference is significant, then we change the model adding one more component to the mixture. Theory is outlined and some examples and applications are presented. Furthermore we shall suggest a quick rule which allows us to assign data points to each component of the mixture,. Software specifically designed to support the entire procedure has been implemented in R computing environment and it will be used to perform all the analysis proposed in the paper.
A Quick Procedure for Model Selection in the Case of Mixture of Bivariate Normal Densities
ISAIA, Ennio Davide;DURIO, Alessandra
2003-01-01
Abstract
In many modeling situations, we often have a choiche. We can add to model complexity to describe some unusual observations or groups of observations or we can remove those observations and fit the rest with a different, perhaps simpler, model. Purpose of this work is to illustrate a procedure in finding the number of the components of a mixture of bivariate normal densities, exploiting in this way the properties of robustness of the estimates based on the Minimum Integrated Squared Error (or Minimum L_2 distance). Each step of the procedure consists in the comparison between the estimates of the parameters of the mixture according to the Maximum Likelihood and Minimum $L_2$ distance criteria. If their difference is significant, then we change the model adding one more component to the mixture. Theory is outlined and some examples and applications are presented. Furthermore we shall suggest a quick rule which allows us to assign data points to each component of the mixture,. Software specifically designed to support the entire procedure has been implemented in R computing environment and it will be used to perform all the analysis proposed in the paper.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
