Mixture structure analysis using the Akaike Information Criterion and the bootstrap

Authors:
Jeffrey L. Solka;Edward J. Wegman;Carey E. Priebe;Wendy L. Poston;George W. Rogers
Affiliations:
Dahlgren Division of the Naval Surface Warfare Center, Systems Research and Technology Department, Advanced Computation Technology Group, Code B10, Dahlgren VA 22448-5100, USA;Center for Computational Statistics, George Mason University, Fairfax, VA 22030-4444, USA;Department of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218, USA;Dahlgren Division of the Naval Surface Warfare Center, Systems Research and Technology Department, Advanced Computation Technology Group, Code B10, Dahlgren VA 22448-5100, USA;Dahlgren Division of the Naval Surface Warfare Center, Systems Research and Technology Department, Advanced Computation Technology Group, Code B10, Dahlgren VA 22448-5100, USA
Venue:
Statistics and Computing
Year:
1998

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Abstract

Given i.i.d. observations x1,x2,x3,…,xn 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.