A moment-based criterion for determining the number of components in a normal mixture model

Determining the number of components is a crucial issue in a mixture model. A moment-based criterion is considered to estimate the number of components arising from a normal mixture model. This criterion is derived from an omnibus statistic involving the skewness and kurtosis of each component. The proposed criterion additionally provides a measurement for the model fit in an absolute sense. The performances of our criterion are satisfactory compared with other classical criteria through Monte-Carlo experiments.