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February 1997 Moment-based oscillation properties of mixture models
Bruce Lindsay, Kathryn Roeder
Ann. Statist. 25(1): 378-386 (February 1997). DOI: 10.1214/aos/1034276634


Consider finite mixture models of the form $g(x; Q) = \int f(x; \theta) dQ(\theta)$, where f is a parametric density and Q is a discrete probability measure. An important and difficult statistical problem concerns the determination of the number of support points (usually known as components) of Q from a sample of observations from g. For an important class of exponential family models we have the following result: if P has more than p components and Q is an appropriately chosen p-component approximation of P, then $g(x; P) - g(x; Q)$ demonstrates a prescribed sign change behavior, as does the corresponding difference in the distribution functions. These strong structural properties have implications for diagnostic plots for the number of components in a finite mixture.


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Bruce Lindsay. Kathryn Roeder. "Moment-based oscillation properties of mixture models." Ann. Statist. 25 (1) 378 - 386, February 1997.


Published: February 1997
First available in Project Euclid: 10 October 2002

zbMATH: 0870.62013
MathSciNet: MR1429930
Digital Object Identifier: 10.1214/aos/1034276634

Primary: 62E10, 62G05
Secondary: 62H05

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 1 • February 1997
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