Mixture structure analysis using the Akaike Information Criterion and the bootstrap

Given i.i.d. observations x(1),x(2),x(3),...x(n) drawn from a mixture of normal terms, one is often interested in determining the number of terms in the mixture and their defining parameters. Although the problem of determining the number of terms is intractable under the most general assumptions, there is hope of elucidating the mixture structure given appropriate caveats on the underlying mixture. This paper examines a new approach to this problem based on the use of Akaike Information Criterion (AIC) based pruning of data driven mixture models which are obtained from resampled data sets. Results of the application of this procedure to artificially generated data sets and a real world data set are provided.